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The deputy speaker of the country's Senate also sent his congratulatory message to the new leader.
Farmajo has urged the new mayor of the capital to perform his duties diligently with patriotism.
A Houthi military spokesman had earlier said that air defenses had brought down a U.S. drone.
In 2013, he refused to swipe t-shirts with an Israeli player in a display of support for Palestinian rights.
The attack was the second in two days as the government tries to stabilize the country's capital.
The surprise decision gives the long-sitting assembly extra time to remain in power and serve.