The investigation into the fatal stabbing of Sir David Amess is being led by counter-terror officers, Essex Police have said.
Official sources have told the PA news agency that a 25-year-old man arrested on suspicion of murder is believed to be a British national with Somali heritage.
The death of Sir David has led to Home Secretary Priti Patel asking all police forces to review security arrangements for MPs “with immediate effect”.
The man arrested following the attack at Belfairs Methodist Church in Leigh-on-Sea near Southend at midday on Friday remains in custody.
Chief constable Ben-Julian Harrington said 69-year-old Southend West MP Sir David was “simply dispensing his duties when his life was horrifically cut short”.
Mr Harrington said: “The investigation is in its very early stages and is being led by officers from the specialist counter-terrorism command.
“We made it clear at the time of the incident that we did not believe there was any immediate further threat to anyone else in the area.
“It will be for investigators to determine whether or not this is a terrorist incident, but as always they will keep an open mind.”
Tory veteran Sir David, who was described by Prime Minister Boris Johnson as “one of the kindest, nicest, most gentle people in politics”, had been an MP since 1983 and was married with five children.
Mr Harrington said officers were called to reports of a stabbing at just after midday.
He said: “The response of the emergency services to this incident was immediate and our officers arrived on scene within minutes.
“When they arrived they found Sir David Amess MP, who had suffered multiple injuries.
“This was a difficult incident, but our officers and paramedics from the East of England Ambulance Service worked extremely hard to save Sir David.
“Tragically he died at the scene. A 25-year-old man was arrested immediately at the scene on suspicion of murder. He remains in custody.
“A knife was also recovered at the scene.”
A spokesman for Home Secretary Ms Patel said she chaired a meeting of the Police, Security and Intelligence Agencies to discuss the incident in Southend and the ongoing response, adding that she had also spoken to the Speaker of the House of Commons.
“The Home Secretary has asked all police forces to review security arrangements for MPs with immediate effect and will provide updates in due course,” the spokesman said.
Sir David’s death echoes that of Labour MP Jo Cox in 2016, who was fatally stabbed as she attended a constituency surgery.
Brendan Cox, Ms Cox’s widower, wrote on Twitter: “This brings everything back.”
Ms Cox’s sister, Kim Leadbeater, Labour MP for Batley and Spen in West Yorkshire, said her partner has asked her to step down.
“It’s so hard because you have a job to do,” she said.
“I find myself now working as a politician and trying to do good things for people and it’s really important you get good people in public life, but this is the risk we are all taking and so many MPs will be scared by this.
“My partner came home and said ‘I don’t want you to do it any more’ because the next time that phone goes, it could be a different conversation.
“There are so many layers to this.
“At the heart of it are David’s family and friends.
“I know for them now that their lives will never be the same again, they will think about this every single day for the rest of their lives.
“Even David’s staff – so many other people today will have been out there trying to do the right thing, trying to do a really important job in public life, and this happens.
“I cannot believe that this has happened.
“It feels very raw for me.
“I know from messages I have received from politicians across the political spectrum, for them it is incredibly raw.”
Tributes have been paid to Sir David since his death was confirmed, with Mr Johnson saying: “I think all our hearts are full of shock and sadness today at the loss of Sir David Amess MP, who 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.
“And the reason I think people are so shocked and saddened is above all he was one of the kindest, nicest, most gentle people in politics, and he also had an outstanding record of passing laws to help the most vulnerable, whether the people who are suffering from endometriosis, passing laws to end cruelty to animals, or doing a huge amount to reduce the fuel poverty suffered by people up and down the country.
“David was a man who believed passionately in this country and in its future.
“And we’ve lost today a fine public servant and a much-loved friend and colleague, and our thoughts are very much today with his wife, his children, and his family.”
The Duke and Duchess of Cambridge said they are “shocked and saddened” by the killing, adding that their “thoughts and prayers” are with Sir David’s family, friends and colleagues.
In a personal tweet from the couple, they said: “We are shocked and saddened by the murder of Sir David Amess, who dedicated 40 years of his life to serving his community.
Our thoughts and prayers are with his family, friends and colleagues. W & C”
A vigil, led by Father Jeffrey Woolnough, is being held at St Peter’s Church on Eastwood Lane, in Leigh-on-Sea.
A photograph of Sir David has been placed at the front of the church.