Sana'a in fourth day of violence, as Houthi fighters and government claim peace talks stall because of the other's intransigence

Fighting has intensified in the Yemeni capital, Sana'a, in the biggest challenge to the country's transition to democracy since former leader Ali Abdullah Saleh was ousted in 2012.

As violence raged for a fourth day the prime minister Mohammed Salem Bassindwa resigned, accusing president Abd Rabbu Mansour Hadi of being "autocratic", senior officials said. State news agency Saba reported Basindawa's resignation, but without giving the reason.

The UN envoy to the conflict-stricken country struggled to broker a last-minute peace deal between Houthi rebels – a militant Shia movement – and the government. The city has reverberated with the sound of shelling, gunfire and fighter jets. Hundreds of people have been displaced from their homes and dozens killed in the fighting, which has spread through much of the west of the capital.

Abdelmalek al-Houthi, the Houthi leader, is calling for the transitional government, in place since 2011, to be dissolved and replaced with a more effective and representative body. He is also calling for fuel subsidies, cut in July, to be reinstated, and for implementation of agreements made during the peace talks, which drew to a close in January.

Hadi, has largely agreed to his demands. But each side claims that the talks have stalled repeatedly because of their counterpart's intransigence.

The government had suspected that peaceful protests by the Houthis in Sana'a might escalate after the militants waged effective campaigns in the north against forces loyal to Major General Ali Mohsen al-Ahmar, a presidential military adviser with conservative Sunni leanings and one of the Houthis' biggest rivals. Mohsen was their principal antagonist during six years of war between the Houthis and the government between 2004 and 2010.

"[It] is not clear that belligerents, especially the Huthis, are ready to sign at this point," said April Alley, a Yemen specialist at International Crisis Group. "They may have military objectives they want to achieve first. We must wait and see."

Yemenis are sceptical that a political solution can be brokered, and worry that if the fighting continues in Sana'a it could trigger Sunni opposition against the group, including from the virulent al-Qaida franchise. "It is not really a surprise," says Alley of the Houthis' military campaign, "but it could be a terrible miscalculation if their fight against political foes in the capital sparks a larger conflagration."