The prime minister is under doctor's orders to rest for 24 hours after hospital treatment for an irregular heartbeat.
Mr Blair is now back in Downing Street
Tony Blair cancelled a planned speech in the House of Commons, although he is going ahead with meetings at Downing Street.
Foreign Secretary Jack Straw is to deliver the statement on the EU summit in the Commons in his place.
The 50-year-old has never suffered heart problems before but was taken to London's Hammersmith Hospital on Sunday, after complaining of chest pains at his Chequers residence and first going to Stoke Mandeville Hospital.
Doctors diagnosed supra ventricular tachycardia - a condition that causes heartbeat irregularities and shortness of breath - and ordered the father-of-four to rest for a day.
He was kept in hospital for more than five hours and treated with a procedure called cardio version, which uses a small electric shock to make the heartbeat return to normal.
Downing Street sought to play down the scare, saying the prime minister planned to be back at his desk full-time on Tuesday morning.
BBC political correspondent Shaun Ley told BBC Radio 4's Today programme that it was "business as usual" as far as Downing Street was concerned.
"They [officials] are stressing that there is no reason to think that this incident of an irregular heartbeat should recur after treatment."
He said they were also stressing there was no direct link being shown between the heart scare and the stress of his job.
"But inevitably that is the kind of question that his colleagues and a great many other people will be asking this morning," our correspondent said.
"Any health incident involving a prime minister in office has got to be an issue for perfectly good and serious reasons, but that obviously doesn't translate into there being any indication that it is anything more serious."
A Downing Street spokesman said: "The hospital says this is a relatively common condition and is easily treated.
"He has suffered no damage and he is fine. There is no reason why this should reoccur. They have advised him to rest for 24 hours."
Mr Blair has been under a great deal of stress in recent months, particularly after the strains of the war in Iraq.
But experts said the condition was more likely to be something that simply affected some people rather than others, instead of being linked to stress.
Dr Duncan Dymond, consultant cardiologist at Barts Hospital, London, told BBC Radio 4's Today programme: "In the grand scheme of things, it's a fairly minor condition - high in nuisance value but low in gravity.
"It can be very frightening for people when it happens, particularly when they don't know what it is."
He said it could happen to healthy people, and once treated was "compatible with a completely normal quality and quantity of life".
Dr Dymond said Mr Blair should have a couple of days rest, but added: "It's by no means set in stone that he will have another attack and there's no real reason for him to stop playing tennis or stop being prime minister based on this."
The US administration was "very glad to hear that he [the Prime Minister] is doing well", National Security Advisor Condolezza Rice told reporters travelling with President George W Bush in Thailand.