"We come together with free men around the world to face down the American Satan," an announcer told the crowd at the Bab al-Yaman entrance to the capital's Old City.

The demonstrators cried "Death to America" and waved banners calling for a boycott of US and Israeli products, in images broadcast by the Huthis' Al-Masirah television.

Huthi official Dhaifallah al-Shami addressed the crowd under giant portraits of Soleimani and top Iraqi military figure Mahdi al-Muhandis, both killed in a US drone strike in Baghdad last Friday.

"The blood of the martyrs Soleimani and Muhandis is not just Iranian or Iraqi but belongs to the Muslim community and to free men around the world," he said.

The Huthis have called for swift reprisals for the killings.

A statement from Huthi authorities read out to the crowd said it was "time for the Americans and Zionists to pack their bags" and leave the region.

The rebels are locked in a five-year conflict with a Saudi-led military coalition.

It was unclear if the Huthi call for reprisals was also directed at Riyadh, which has stepped up efforts to end Yemen's conflict amid a lull in Huthi attacks on the kingdom.

Last September, the Huthis claimed responsibility for strikes against two major oil sites in eastern Saudi Arabia. Riyadh and Washington accused Iran of being behind the attacks, despite Tehran's denials.