But a spokeswoman for the former prime minister said he had been told to follow guidance on "international conferences", having been invited by US officials to attend a White House event held over the Israel-UAE peace deal.
"He (Mr Blair) was not refused exemption by the UK Government," the spokeswoman said.
"He was told to follow the guidance on international conferences which he did; the US Government had cleared the visit because it was for the diplomatic conference at the White House.
"We believe he followed all UK and US government guidelines as advised.
"Mr Blair was tested for Covid before departing the UK, on arrival at the White House, when he returned to the UK and has been tested several times since."
Tony Blair in recent years
Tony Blair in recent years
Former prime minister Tony Blair during a speech to mark the 120th anniversary of the founding of the Labour party, in the Great Hall at King's College, London.
Former prime minister Tony Blair, arrives for the funeral of Frank Dobson at St Pancras Church in London.
Former Prime Minister Tony Blair on stage during the Final Say rally at the Mermaid Theatre, London.
Former Prime Minister Tony Blair in Downing Street arriving for the Remembrance Sunday service at the Cenotaph memorial in Whitehall, central London.
File photo dated 02/09/19 of former prime minister Tony Blair, who has said Tory and Labour MPs would both face a "big risk" by fighting a general election on the issue of Brexit.
Former prime minister Tony Blair, during a Service of Thanksgiving for the life and work of Lord Ashdown at Westminster Abbey in London.
Former prime minister Tony Blair gives a speech at the Institute for Government in central London where he will call for Labour to oppose any move by Boris Johnson to hold an emergency general election until Brexit has been resolved.
Prime Minister Theresa May speaks alongside former prime ministers David Cameron, Tony Blair, and Gordon Brown and former leader of the Liberal Democrats Nick Clegg during a service of thanksgiving for the life and work of former Cabinet Secretary Lord Heywood at Westminster Abbey in London.
Former prime minister Tony Blair with Prime Minister Theresa May as they leave following a service of thanksgiving for the life and work of former Cabinet Secretary Lord Heywood at Westminster Abbey in London.
Former prime minister Tony Blair makes a speech on Brexit at the British Academy in London.
Former Prime Minister Tony Blair during the remembrance service at the Cenotaph memorial in Whitehall, central London, on the 100th anniversary of the signing of the Armistice which marked the end of the First World War.
Lisbon, 07/11/2018 - Web Summit 2018 was held at the Altice Arena in Lisbon from 5 to 8 November. Tony Blair (Filipe Amorim / Global Imagens)
Former prime minister Tony Blair speaking at the launch of the Resolution Foundation's annual Living Standards Audit in central London.
Former prime minister Tony Blair arrives to give a speech on poverty and inequality at the launch of the Resolution Foundation's annual Living Standards Audit in central London.
Former Prime Minister Tony Blair talking about the Good Friday Agreement in London.
Former Prime Minister Tony Blair in conversation with Professor Anand Menon during the Changing Europe conference on Brexit in central London.
Former Prime Minister Tony Blair speaking during the Changing Europe conference on Brexit in central London.
Former Prime Minister Tony Blair and his wife Cherie walk through Downing Street on their way to the annual Remembrance Sunday Service at the Cenotaph memorial in Whitehall, central London.
Tony Blair addresses a conference on Brexit in the Druids Glen Hotel, Wicklow, Ireland.
Tony Blair at a Brexit meeting in Wicklow, Ireland.
Former Prime Minister of the United Kingdom Tony Blair addressing the 2017 American Israel Public Affairs Committee (AIPAC) Policy Conference in Washington, D.C. on March 26, 2017. (Photo by Michael Brochstein) *** Please Use Credit from Credit Field ***
Former Prime Minister Tony Blair during his speech on Brexit at an Open Britain event in central London.
Former Prime Minister Tony Blair holds a press conference at Admiralty House, London, where responding to the Chilcot report he said: "I express more sorrow, regret and apology than you may ever know or can believe."
Former prime minister Tony Blair and wife Cherie arrive at St Paul's Cathedral in London for a national service of thanksgiving to celebrate the 90th birthday of Queen Elizabeth II.
Former prime ministers Sir John Major (left) and Tony Blair walk across the Peace Bridge in Londonderry following a Remain campaign event at the University of Ulster in Londonderry.
Former prime minister Tony Blair during a Remain campaign event at the University of Ulster in Londonderry.
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The spokeswoman said all Covid-19 tests had been negative, adding that Mr Blair did not attend any other meetings during his trip.
Government guidance states that diplomats and representatives at international conferences are granted "privileges and immunities", meaning they are not required to self-isolate if their work is confirmed as essential.
A Foreign, Commonwealth and Development Office (FCDO) spokeswoman said: "The FCDO provides travel exemptions to diplomats travelling on business relating to the interests of the UK, representatives of international organisations, and their families and dependents.
"Those issued an exemption will not need to self-isolate."
Mr Blair flew to Washington DC on September 14 and returned on September 16, according to the Sunday Telegraph, which reports he was seen leaving Harry's Bar in Mayfair on September 26.
Conservative MP David Jones, a member of Parliament's public administration committee, told the newspaper it was "hard to see" how Mr Blair could rely on claiming he had been tested "when we haven't got a testing regime".
"It sets an appalling example to travellers if a former prime minister appears to flout the rules in such a flagrant manner," he said.