Prime Minister Mohamed Basindawa stepped aside, accusing President Abdrabuh Mansur Hadi of being "autocratic", senior officials said.
State news agency Saba reported Basindawa's resignation, but without giving the reason.
Mohammed Abdulsalam, spokesman for the Ansarullah rebels, also known as Huthis, confirmed on his Facebook page that the seat of government had been taken.
Earlier, shelling and gunfire in the north of Sanaa was heard across the city, as Sunni militiamen and troops battled the rebels, prompting an exodus of terrified residents, an AFP correspondent reported.
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There was no let-up in the fighting yesterday night despite Hadi ordering an after-dark curfew.
The clashes centred on the campus of Al-Iman University, a bastion of Sunni Islamists that the Shiite rebels have been trying to capture, witnesses said.
The violence came despite UN envoy Jamal Benomar announcing late yesterday that a deal had been reached after "intense consultations with all the political parties, including Ansarullah".
Benomar did not specifically mention a ceasefire, nor did he say when a deal would be signed, although he said preparations were under way for the signing.
Forces allied to the government have been battling to halt the rebels, who swept into Sanaa from their mountain stronghold in the far north last month and set up armed protest camps across the capital to press their demands.
Hadi has denounced the rebel offensive as a "coup attempt", but agreed to involve the rebels in the formation of a new government to replace the unpopular administration that imposed austerity measures, including a fuel price hike, earlier this year.
But the rebels have also demanded posts in key state institutions as part of a push for greater political clout.