Witnesses said the heavily armed gunmen were also clashing with troops outside the residence of Hadi, who was reportedly inside receiving visitors at the time of the attack.
"The Yemeni president is under attack by militiamen who want to overthrow the regime," Information Minister Nadia Sakkaf said on Twitter.
The fresh unrest came after the Huthi militiamen, who have tightened their grip on Sanaa since overrunning it unopposed in September, surrounded the prime minister's residence at the end of a bloody day on Monday.
The United Nations Security Council is to hold closed door consultations about the worsening crisis Tuesday, with special envoy Jamal Benomar to report on the latest developments.
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Pitched battles had erupted on Monday near the presidential palace and in other parts of Sanaa, before a ceasefire was agreed between ministers and a Huthi representative.
At least nine people were killed, including fighters from both sides, and 67 wounded, as the militia seized an army base overlooking the complex and took control of state media.
Prime Minister Khalid Bahah escaped to his residence, where he has lived since taking office in October, after his convoy came under fire from Huthi fighters.
Huthi gunmen took up positions outside the residence late on Monday and were in control of all three of its entrances, government spokesman Rajih Badi told AFP.
After a lull overnight, fighting re-erupted on Tuesday near Hadi's residence in western Sanaa when the Huthis attempted to set up a new checkpoint close by and were confronted by troops, the witnesses said.
Tensions have been running high in Sanaa since the Huthis on Saturday abducted Hadi's chief of staff, Ahmed Awad bin Mubarak, in an apparent move to extract changes to a draft constitution that he is overseeing.
Mubarak is in charge of a "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.