The 69-year-old, who has been an Tory MP since 1983, was fatally injured at Belfairs Methodist Church in Leigh-on-Sea near Southend at midday on Friday.
A 25-year-old man has been arrested on suspicion of murder.
All flags at the Senedd, the Welsh Parliament, are also to be lowered to half-mast following the death of Sir David.
Speaker of the Welsh Parliament, Elin Jones MS, said she was “deeply shocked and saddened” by news of the fatal attack.
Scotland’s First Minister Nicola Sturgeon said the news was “awful beyond words”.
She wrote on Twitter: “My thoughts and deepest condolences are with David’s family, friends and colleagues. May he rest in peace.
"Elected representatives from across the political spectrum will be united in sadness and shock today.
"In a democracy, politicians must be accessible and open to scrutiny, but no-one deserves to have their life taken while working for and representing their constituents.”
Prime Minister Boris Johnson said he was “one of the kindest, nicest, most gentle people in politics”.
Speaking on Friday evening, Mr Johnson said: “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.”