Boris Johnson said some of his outspoken comments had been "taken out of context" as he faced hostile questions in his first press conference as foreign secretary.
Appearing with US Secretary of State John Kerry, he played down remarks about Barack Obama and Hillary Clinton.
Mr Kerry said the UK's vote to leave the EU posed "complicated questions" regarding future trade deals.
Earlier, Mr Johnson and Mr Kerry held talks focusing on Syria.
They will also meet European foreign ministers before talks with Saudi Arabian and United Arab Emirate representatives about the situation in Yemen.
Until his appointment as foreign secretary by new Prime Minister Theresa May, Mr Johnson wrote a weekly column in the Daily Telegraph.
In 2007, he wrote that Mrs Clinton, the Democrat candidate for US president, was "like a sadistic nurse in a mental hospital".
He also faced criticism ahead of the EU referendum for remarks about President Obama's "part-Kenyan" ancestry.
Asked whether he would like to apologise, he said: "We can spend an awfully long time going over lots of stuff that I've written over the last 30 years," adding that they had all been "taken out of context" and insisting the focus should be on Syria and the other issues being discussed.
Pressed on his comments, by US journalists, he said it would take too long to apologise to everyone mentioned in the "rich thesaurus" of things he had said.
Mr Johnson and Mr Kerry both emphasised that the "special relationship" between their countries remained strong.
Asked about President Obama's remark - made before the EU referendum - that the UK would be "at the back of the queue" on trade deals if it voted to leave, Mr Kerry said it could take "at least a couple of years" to reach an agreement as the UK could not sign a new deal while it remained an EU member.
He said Mrs May had "hit the ground running" as prime minister, adding: "The United States of America depends on a strong United Kingdom."
On Syria, Mr Johnson said a "clear plan" was in place but that the situation on the ground was "dire".
He said it had always been his view that Syria's President, Bashar al-Assad, had to step aside as part of a peace plan, and that Russia had a "unique ability" to press him to "end the carnage".
EU foreign affairs chief Federica Mogherini will also participate in the talks in London on Syria.
Peace talks on Syria, co-sponsored by the US and Russia, have not formally examined whether any deal could require President Assad's departure from the country.
Mr Johnson, who made his debut on the international stage in Brussels on Monday, when he met EU foreign ministers, will travel to Washington on Thursday for talks on combating so-called Islamic State.