Yemeni forces loyal to President Abd-Rabbu Mansour Hadi made gains on Sunday in the southwestern city of Taiz after days of battles with Houthi fighters, a local official and residents said.

The Hadi supporters, who have been backed by air strikes by a Saudi-led coalition since March, made particular progress around the presidential palace, the locals said. The complex has changed hands several times and been all but destroyed in the fighting.

Medical sources said 13 Houthi fighters were killed in the fighting in Yemen's third largest city. So were eight fighters loyal to Hadi. Reuters could not independently verify their accounts.

The Arab coalition is trying to restore Hadi's government and fend off what it sees as creeping Iranian influence. The Houthis are allied to Iran and also have support from forces loyal to former president Ali Abdullah Saleh.

Several residents said Hadi loyalists had taken control of a number of mountain peaks on the southern approach to Taiz, Yemen's cultural capital.

At least 5,600 people have been killed in Yemen, the poorest country on the Arabian Peninsula, and the United Nations says the humanitarian situation, exacerbated by the Arab coalition's blockade of Yemeni ports, grows worse every day.

Houthi gunmen prevented convoys of medical supplies from entering an enclave of Taiz, the aid group Medecins Sans Frontieres said. Residents there reported the rebels were also blocking the entry of food, water and fuel to the area, it said.

"After weeks of negotiations, we have made no progress in convincing officials of the need to provide impartial medical assistance," MSF’s emergency manager for Yemen, Karline Kleijer, said in a statement.

The United Nations envoy to Yemen said on Friday he was arranging face-to-face negotiations between the Yemeni government and Houthi rebels. But he warned the conflict had left most of the country in dire need.

The Saudi-led coalition has gained ground in southern Yemen, and Hadi's government officially returned to Aden after southern fighters and coalition forces drove the Houthis out in July.

But Houthi forces remain in control of much of the country despite almost daily air strikes. A suicide attack earlier this month forced the government to relocate to Saudi Arabia while efforts were being made to restore security in the city.

Sudanese forces arrived in Aden last week to reinforce the coalition troops and have deployed around the airport and the city's four ports. Hadi supporters have begun effort to prevent gunmen from moving around with weapons.

A security official in Aden told Reuters on Sunday that armed tribesmen raided the central prison in Aden, killing a guard and wounding another, to free a prisoner held for an earlier attack in the city.

Reuters