PC Palmer was one of five people who died, including the suspected assailant, in the heart of London.
The meeting in Whitehall was addressed by Metropolitan Police Assistant Commissioner for Specialist Operations Mark Rowley, Britain's most senior anti-terrorist police officer.
Constable Palmer had been a member of the police force for 15 years and had previously served with the British Royal Artillery.
"He was supported by armed colleagues who shot and killed the attacker".
Paying tribute to the officer, the Mayor of London Sadiq Khan said: "Keith Palmer was killed while bravely doing his duty - protecting our city and the heart of our democracy from those who want to destroy our way of life".
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He stabbed the mum-of-two 15 times and then shot her three times.
"He was someone who left for work today expecting that he would return home at the end of his shift", Rowley said of Palmer.
"Heartbroken" former colleague Conservative MP James Cleverly paid tribute to the "lovely man" he had known for a quarter of a century.
"We will all move forward together, never giving in to terror and never allowing the voices of hate and evil to drive us apart", Mrs May said.
A total of five people - including the perpetrator - died and around 40 others were injured in the horrific attack.
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Lights on the Eiffel Tower in Paris were switched off at midnight in solidarity with victims of the attack.
May was in parliament at the time of the attack and was seen being ushered away in a silver vehicle as what sounded like gunfire rang out, British media reported.
At least 20 people were wounded and some were said to have sustained "catastrophic" injuries.
Press Association news agency photos believed to be of the attacker lying on an ambulance stretcher showed he was wearing black clothes and had a beard.
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