The Huthi militiamen, known as Ansarullah, had been deploying reinforcements near the presidential palace, which remained under regular army guard after they overran Sanaa in September.
The presidential guard too deployed reinforcements to the streets surrounding the palace complex and outside the residence of President Abdrabuh Mansur Hadi, witnesses said.
Residents fled the intense fighting, witnesses said.
Tensions have been running high in Sanaa since the Huthis abducted Hadi’s chief of staff Ahmed Awad bin Mubarak on Saturday, in a bid to extract changes to a draft constitution he has been overseeing.
Mubarak heads the national dialogue set up after veteran strongman Ali Abdullah Saleh was forced from power in February 2012 following a year of bloody Arab Spring-inspired protests.
The Huthis said they had seized the top aide to prevent the violation of a UN-brokered agreement they reached with the president after their takeover of the capital last September.
The deal provided for the formation of a new government and the appointment of Huthi advisers to the president.
In return, it stipulated that the Huthis withdraw from key state institutions they had seized.
Since their takeover of the capital, the Huthis have pressed their advance into mainly Sunni areas south of Sanaa, where they have met deadly resistance from Sunnis, including Al-Qaeda loyalists.
The turmoil has raised fears that Yemen, which neighbours oil-rich Saudi Arabia and lies on the key shipping route from the Suez Canal to the Gulf, may become a failed state similar to Somalia.
Yemen has been dogged by instability ever since the 2011 protests that forced Saleh to step down, with the Huthis and Al-Qaeda battling to fill the power vacuum.