The British monarch was joined by other senior royals including Prince Charles and the Duchess of Cornwall as she welcomed the dignitaries.
The Aga Khan was also accompanied by members of his family, including his brother Prince Amyn, his daughter Princess Zahra, his sons Prince Rahim, Prince Hussain and Prince Aly Muhammad, and his daughter-in-law Princess Salwa.
Prince Shah Karim Al Hussaini Aga Khan began a year-long jubilee to commemorate the 60th anniversary of his leadership in July last year.
In January, he travelled to the UAE where he met with Sheikh Mohammed bin Zayed, Crown Prince of Abu Dhabi and Deputy Supreme Commander of the UAE Armed Forces.
The pair discussed ways to boost co-operation on humanitarian issues and development projects needed in disadvantaged areas of the world.
He also met Sheikh Mohammed bin Rashid Al Maktoum, Vice President and the Ruler of Dubai, and Sheikh Nahyan bin Mubarak, Minister for Tolerance, during his UAE trip.