Speaking outside Southend police station, the Home Secretary said face-to-face surgeries would continue.
“We will carry on,” she said.
“We live in an open society, a democracy. We cannot be cowed by any individual or any motivation… to stop us from functioning, to serve our elected a democracy.”
Earlier Prime Minister Boris Johnson and Labour leader Keir Starmer laid flowers at Belfairs Methodist Church, where Sir David was killed.
On Friday, Mr Johnson said Sir David “was killed in his constituency surgery in a church after almost 40 years of continuous service to the people of Essex and the whole of the United Kingdom.”
A suspect has been arrested.
Government sources have said he is a British national who, from initial inquiries, appears to be of Somali heritage.
In a statement, the Met said Senior National Coordinator for Counter Terrorism Policing, Deputy Assistant Commissioner Dean Haydon, had formally declared the incident as terrorism.
Labour MP Diane Abbott: ‘I would prefer to meet people behind a screen’
Veteran Labour MP Diane Abbott said she would “prefer” to meet constituents behind a screen to prevent possible stab attacks.
But the former shadow home secretary said having constituency surgeries observed by police could risk putting people off from visiting their local MP.
Ms Abbott told BBC Radio 4’s PM programme: “It’s very difficult. I’ve been talking to colleagues. There was one in north London who was telling me that because of death threats she had a police officer outside her advice session – and a police car, in fact.
“Well of course the number of people coming to see her dropped right down.
“You don’t want to have a set-up which is so off-putting to ordinary people that just want help. So I wouldn’t support airport-style screening.
“I would prefer going forward to meet constituents behind a screen, as we have now for Covid and so on – that might be quite complicated to arrange but at least you know someone’s not going to just lean over the desk and stab you, which could happen now.”
Sir David Amess family ‘raw with emotion’, says church minister
Reverend Clifford Newman, of Belfairs Methodist Church – where Sir David Amess was killed – said the MP held his surgery there because he wanted to be where his constituents were.
He said: “The church is a natural place where people look to.
“He was a person who was for the community and wanted to be in the community, and so a church is obviously a community place.
“It’s a Methodist church, so it’s not like Catholic or Anglican churches, it’s much less formal, but there are pews within the church and it has a couple of community halls.”
The reverend, who did not know Sir David personally, said he was at home when the attack happened, and rushed to the scene when he heard about it to “gauge where people are”.
“There’s a lot of raw feeling obviously with the family and obviously with our church members, but also within the community itself,” he added.
MP Kieran Mullan: ‘We mustn’t be forced to do things differently’
Kieran Mullan, the Tory MP for Crewe and Nantwich, tweeted: “Surgery today, we must not let people force us to do things differently.
“David would not have wanted that.”
Craig Williams, MP for Montgomeryshire, also held a surgery on Saturday alongside his Conservative colleague from the Welsh Parliament, Russell George.
Mr Williams tweeted: “Busy surgery with @russ_george in #Guilsfield this morning. Thought of Sir David Amess throughout.
“A special shout out to @DyfedPowys for their presence and reassurance. #Montgomeryshire”
Tory MP Bob Blackman: ‘It’s quite scary, particularly for staff’
Conservative MP Bob Blackman said MPs will now be “wary” of what they do in light of Sir David Amess’s death.
He told the PA news agency: “I’ve had demonstrations that were outside my office from various different groups at different times, which is quite scary, particularly for staff.
“I think it’s like everything else, you’ve just got to be wary of what you do now, because, unfortunately, we don’t know what else is going to happen.”
Labour MP Naz Shah: ‘I’ve had so many death threats. It could have been any one of us’
Labour MP Naz Shah, who has previously been targeted with racist abuse, said there was “no right or wrong answer” over whether or not MPs should continue holding their surgeries.
Ms Shah, who represents the Bradford West constituency, told the PA news agency: “I think it’s all about individuals, isn’t it?
“I’ve had so many death threats, and it could have been any one of us. It’s really close to home. I just think you’ve got to respect every MP. Some will have the ‘Yes, we’re going to carry on’ view, and some people won’t feel comfortable.
“At this time, I think there’s no right or no wrong answer to whether we should do surgeries or not. How people feel is individual to them really, depending on their personal circumstances.”
Mosques condemn killing of MP Sir David Amess
The fatal stabbing of MP Sir David Amess has been condemned as an “indefensible atrocity” in a joint statement from all of Southend’s mosques, as police said the attack may be linked to Islamist extremism.
Faith leaders said that the father-of-five was an “upstanding friend to our Muslim community” and attended key events, including weddings, mosque openings and the launch of the town’s first Muslim Scout group.
In a statement published on the Essex Jamme Masjid website, on behalf of “all Southend mosques”, they said their thoughts and prayers were with Sir David’s family, friends and colleagues.
“Sir David’s murder was an indefensible atrocity, committed on the grounds of a place of worship and we condemn it in the strongest possible terms,” the statement said.
“This act was committed in the name of blind hatred, and we look forward to the perpetrator being brought to justice.”
Iranians: Sir David Amess an ‘enemy of many dictators’
An Iranian opposition group has paid tribute to Sir David Amess, describing the MP as a “human rights champion” and an “enemy of many dictators”.
Hossein Abedini was among several members of the National Council of Resistance of Iran who laid flowers and framed photos of Sir David near Belfairs Methodist Church in Leigh-on-Sea, Essex, where the MP was stabbed to death.
Mr Abedini told the PA news agency: “Sir David had a very important role in supporting the people of Iran, the uprisings happening in Iran, the Iranian refugees in Camp Ashraf.”
As part of this, Sir David had recently called on the Government to ban Iran’s president Ebrahim Raisi, a hardline cleric, from attending the Cop26 global climate summit in Glasgow, Mr Abedini said.
Ex-minister Chris Skidmore: ‘I recognise the threat but this is the British way’
Former minister Chris Skidmore said he has continued to hold face-to-face constituency surgeries despite someone previously being put behind bars for threatening to kill him.
The Conservative MP for Kingswood in South Gloucestershire said he holds two types of surgeries: one where verified constituents book to see him at his office and a second where he holds drop-in sessions, including at supermarkets where shoppers are invited to talk to their MP over the shop tannoy.
Mr Skidmore, a former universities minister, told the PA news agency: “I would still want to continue those.
“I’ve been an MP now for 11 years, I won the seat and have taken it up to an 11,000 majority by doing these type of visible, community-based appearances.
“I feel as a member of Parliament who was born and grew up in my constituency, it feels absolutely natural that I would continue to hold in-person events.
“I’ve had someone in the past who has been in prison for threatening to kill me, so I recognise these threats, but it is a cornerstone of our British way of life when it comes to our democracy – very few countries have this.”
Tory MP Alec Shelbrooke holds surgery saying killing cannot diminish deep relationship with constituents
Alec Shelbrooke was among the MPs who held constituency surgeries as usual on Saturday, less than 24 hours after the death of Sir David Amess.
The Conservative MP for Elmet and Rothwell tweeted: “We cannot let events like this diminish the deep relationship between an MP and their constituents.
“This is a relationship I value deeply: I want my constituents, regardless of whether they voted for me or not, to be able to approach me in the street, in the pub, at the supermarket or at one of my surgeries.”
Irish president Michael D Higgins sends ‘deepest sympathies’
The president of Ireland has extended condolences to the family of Sir David Amess.
Michael D Higgins said the Conservative MP was killed while carrying out a fundamental role of a politician – helping their constituents.
Mr Higgins said: “May I express my deepest sympathies to the family, friends, colleagues in Parliament and constituents of Sir David Amess, who was murdered while carrying out that most fundamental act of a politician, meeting with his constituents, assisting them with their issues.
“All of those who value representative politics will think also today of the family of the late Jo Cox, who was taken from her family in June 2016.
“I know that all those who serve the people of the United Kingdom will have been deeply affected by these two murders and on behalf of the Irish people, I send them our deepest sympathies.”
Meanwhile, the British-Irish Parliamentary Assembly has cancelled a scheduled plenary meeting at Westminster on Monday as a mark of respect for Sir David.