Sheikh Mohammed bin Rashid met Yemen's prime minister, Maeen Abdulmalik Saeed, at Expo 2020 Dubai on Monday.
The Vice President and Ruler of Dubai toured Yemen's pavilion at the world fair with Mr Saeed.
Sheikh Mohammed spoke of the meeting on Twitter, praising the “honour, honesty, pride and brotherhood” of the people of Yemen.
Mr Saeed held high-level talks with UAE leaders during his trip to the Emirates.
On New Year's Eve, he met Sheikh Mohamed bin Zayed, Crown Prince of Abu Dhabi and Deputy Supreme Commander of the Armed Forces, in the capital.
During that meeting, the pair discussed efforts to forge closer ties between their nations and reviewed the humanitarian situation and latest developments in Yemen.
Sheikh Mohamed said the UAE was committed to ensuring Yemen's security and stability.
Mr Saeed thanked the UAE for its developmental and humanitarian support for Yemen, which includes contributions towards restoring vital facilities and developing infrastructure.
He also praised the efforts of the Arab Coalition to Support Legitimacy in Yemen, led by Saudi Arabia, and its role in supporting the Yemeni people.