PM Boris Johnson's said that the suspension would take place regardless of the outcome of a government-led vote on holding a snap election next month.
The 93-year-old monarch was dressed in tweeds and wearing a headscarf at the time and was walking with one of her protection officers when the tourists asked if she had ever met the queen.
Queen Elizabeth II has already given the go-ahead to shutter parliament between mid-September and October 14.
It happened as the Queen was showing the President and his wife around an exhibition at the palace picture gallery of American artefacts on Monday.
The 37-year-old royal, who gave birth to the couple's first baby Archie earlier this month, will not join the rest of the royals during a series of events during the three-day visit beginning June 3.
Lady Gabriella Windsor(38), daughter of the monarch's first cousin Prince Michael of Kent tied the knot with financier Thomas Kingston.
The 92-year-old monarch received Ghanashyam at Buckingham Palace for the presentation of letters of credence ceremony, which marks the formal launch of a new envoy's tenure in the UK.
He surrendered his licence on Saturday, the palace said The Prince's decision to hand over his driving licence was entirely his own and he will be driven from now on, it added.
With the UK set to exit the 28-member European Union (EU) on March 29, the government fears riots in the capital city as a result of the Brexit deal.
Speaking to members of the Women's Institute (WI) near her Sandringham estate in eastern England, the 92-year-old said people should never lose sight of the bigger picture.
Images published in Sunday newspapers appeared to show him behind the wheel of a replacement Land Rover Freelander on his wife Queen Elizabeth II's private Sandringham estate on Saturday.
Pictures from the scene showed Tata Motors' Land Rover laying on its side with debris scattered around it.
US President Donald Trump's interview with Good Morning Britain was broadcast Monday.
Sting, Tom Jones, Craig David and Kylie Minogue are among singers performing at the celebration at Royal Albert Hall, billed as the "Queen's Birthday Party.
As fifth and soon to be sixth in line to the British throne, Harry is among a handful of senior royals who must seek the monarch's permission to marry under the Succession to the Crown Act.