During the meeting, Sheikh Mohammed received a letter from King Salman on ways to strengthen bilateral relations between the countries.
The letter also contained wishes of good health for the President, Sheikh Khalifa.
Sheikh Mohammed conveyed Sheikh Khalifa's greetings to King Salman and Crown Prince Mohammed bin Salman, wishing them good health and wellness.
Also in attendance was the diplomatic adviser to Sheikh Khalifa, Dr Anwar Gargash, Minister of Cabinet Affairs Mohammad Al Gergawi and Reem Al Hashimy, Minister of State for International Co-operation and director general of Expo 2020 Dubai.
Sheikh Mohammed also met President Carlos Alvarado Quesada of Costa Rica.
The meeting took place at the Costa Rica pavilion on Monday.
Sheikh Mohammed was accompanied by Sheikh Maktoum bin Mohammed, Deputy Prime Minister, Minister of Finance and Deputy Ruler of Dubai.
Mr Alvarado is on an official visit to the UAE.