The Shiite group held a rally attended by about 30,000 tribal leaders in Sanaa on Friday, where they delivered a communique warning President Abd-Rabbu Mansour Hadi that "all options are open" if he failed to form a government.
"Our next meeting will be at the headquarters of the decision making," said Deif Allah Rassam, spokesman of the 'Popular Tribal Alliance."
A second speaker at the rally, Naguib al-Mansouri, called for the formation of a "salvation military council".
The formation of an agreed government is part of a UN deal to reach a peaceful settlement to Yemen's political crisis.
Al Jazeera's Omar al-Saleh, reporting from Sanaa, said that the message from the tribal meeting was quite clear.
"It is a very significant development and it only indicates who holds the power in this country," he said.
"Now the aim of that tribal gathering is very clear. They wanted to send several messages to the political leaders and the regional powers. The first, Houthis are not on their own. They have the tribal support," he said, adding that in Yemen tribal affiliations are very important to be able to rule.
"Second, they could be trying to pressure the prime minister-deisgnate and the president to form a new unity government."
Al-Saleh said that official reaction to the ultimatum had not been made public, despite rumours circulating the day before that the tribal gathering would takle place on Friday.
Al-Saleh said that it is expected the presidency will reject the ultimatum and stated that a top UN diplomat told Al Jazeera that the move will be seen as a manoeuvre to exert pressure on the political parties concerned.