Mr Trump moved slightly nearer but then stood still in front of the queen, meaning she had to navigate her way around him so they could walk side by side.
It was also the monarch's first in-person meeting with a foreign leader in more than a year, after she was forced into self-isolation because of the coronavirus pandemic.
During her first meeting with President Dwight D. Eisenhower hosted in the states, in 1957, Queen Elizabeth saw her first American college football game - and met former President Herbert Hoover on the same trip.
Her Majesty, 95, looked radiant in the smart ensemble - a departure from her usual bright colour palette - which she teamed with her usual black Launer handbag and black patent leather shoes with silver buckles. Prince Philip, Duke of Edinburgh, died in April.
While posing for a group photo with other G7 leaders, Queen Elizabeth cracked a joke. " "We could fit the White House in the courtyard" " of Windsor Castle, Biden recounted telling her. Biden said he extended an invitation for the queen to visit the White House.More news: Biden urges G-7 leaders to call out, compete with China
He followed the advice his mother gave him before he first met Queen Elizabeth in 1982, CNN reports.
During her 69 years on the British throne, the longest reign of any English monarch, there have been 14 US presidents, of which Elizabeth has met all bar Lyndon Johnson. It's one indication of the importance the monarch, who came of age following World War II, places on this "special" transatlantic relationship.
Her Majesty has met all but Lyndon Johnson.
However, last year, it was cancelled due to the pandemic and it was instead marked with a ceremonial tribute at Windsor.
Mr Biden has a meeting with Mr Putin next week.
On Friday, the queen surprised the G-7 leaders by traveling to the coastal southwestern county of Cornwall to take part in a welcome event alongside Prince Charles, Prince William and Kate, the duchess of Cambridge.More news: At least 13 people wounded in Austin, Texas shooting
Kate, duchess of Cambridge, left, and First Lady Jill Biden share a laugh during a visit to Connor Downs Academy in Hayle, England, on Friday.
He confirmed he's invited the Queen to the White House. "Anyway, she was very gracious". She has welcomed four other United States presidents to Windsor Castle, where she has been isolating during the coronavirus pandemic. "I hope that will be soon".
Before boarding Air Force One, the President spoke for a while on the tarmac with some guests and then bid farewell to the first lady, who is returning to Washington.
"No I didn't. We've been busy". "We were talking education".
In talks lasting just under three-quarters of an hour, the pair also discussed despots and autocrats - Presidents Putin of Russian Federation and Xi of China - although President Biden stopped short of revealing the monarch's view of the pair.More news: Major International Sting Operation Leads To 800 Arrests