He paid his sincere condolences, a statement from the British Embassy read.
"His Royal Highness also offered his warmest congratulations to His Highness Sheikh Mohamed bin Zayed Al Nahyan on his appointment as President of the United Arab Emirates and Ruler of Abu Dhabi."
He was pictured with Sheikh Mansour bin Zayed, Deputy Prime Minister and Minister of Presidential Affairs and other members of the ruling family at Mushrif Palace.
Sheikh Mohammed met a number of international leaders and officials at the palace on Monday.
Among those offering condolences were Roman Golovchenko, Prime Minister of Belarus, Ali Asadov, Prime Minister of Azerbaijan and Ahmed Ali Abdullah Saleh, son of Yemen's late former president Ali Abdullah Saleh.
Prince Charles earlier expressed his condolences in a call with Sheikh Mohamed, in which he also conveyed his best wishes over his election as president.
Queen Elizabeth II also sent a message of support to Sheikh Mohamed, sharing her sadness over Sheikh Khalifa's death.
“He will be long remembered by all who work for regional stability, understanding between nations and between faiths, and for the conservation cause,” she said in the message.
The death of Sheikh Khalifa was announced on Friday.
Monday marked the third day of mourning in the Emirates.
Dozens of leaders and senior officials have travelled to Abu Dhabi in recent days to pay tribute to Sheikh Khalifa, who had served as president since 2004.
Qatar's Sheikh Tamim bin Hamad was pictured walking through Abu Dhabi airport with Sheikh Mohamed on his first visit since 2016.
Israel's President Issac Herzog paid his respects along with two senior ministers. Britain's Boris Johnson travelled from London to meet the new president.
German President Frank-Walter Steinmeier and Morocco's Prince Moulay Rachid also met Sheikh Mohamed in person.
US Secretary of State Antony Blinken landed in Abu Dhabi on Monday morning.
Meanwhile, US Vice President Kamala Harris landed briefly in Germany on Monday morning before continuing her journey to the UAE.
Ms Harris will lead a US delegation which includes other high level officials such as Secretary of Defence Lloyd Austin, CIA Director Bill Burns, Climate Envoy John Kerry, National Security Adviser to the Vice President Philip Gordon, White House Middle East co-ordinator Brett McGurk, White House Senior Director for the Middle East and North Africa, Barbara Leaf, and Sean Murphy, Charge d’Affaires at the US Embassy Abu Dhabi.
Prince William made his first official visit to the UAE in February.
During the landmark tour, he met Sheikh Hamdan bin Mohammed, Crown Prince of Dubai, visited the Abu Dhabi mangroves and observed how Dubai’s Jebel Ali Port tackles illegal wildlife trade.
A highlight of the trip was at Expo 2020 Dubai, where Prince William was welcomed by cheering crowds.