Heavy clashes and air strikes in Yemen's third city Taez left at least 36 fighters dead on Sunday, army sources said, as aid workers struggled to make medical deliveries.

The fighting between Saudi-backed pro-government forces and Shiite Huthi rebels and their allies killed at least 21 rebels and 15 loyalists, the sources said.

New clashes broke out when loyalist forces tried to take back a presidential palace on a hill overlooking the city's east.

Loyalists control the centre of Taez, encircled by the Huthi rebels and allied forces loyal to ousted president Ali Abdullah Saleh.

The city in central Yemen has been a key battleground as forces loyal to President Abedrabbo Mansour Hadi seek to regain ground from the Iran-backed Huthis.

In a statement on Sunday, aid group Doctors Without Borders (MSF) said essential medical supplies it hoped to deliver to a besieged enclave of the city were being blocked.

"It is very frustrating that, after weeks of negotiations, we have made no progress in convincing officials of the need to provide impartial medical assistance to the victims of the ongoing fighting within this enclave," Karline Kleijer, MSF's emergency manager for Yemen, said.

She said that this was despite MSF's support to health facilities in Huthi-controlled areas.

Only six of 20 hospitals in the city of more than 600,000 continue to function due to the conflict, and often only partially, MSF said.

"They lack staff, fuel and essential medicines, and are overwhelmed by the high numbers of wounded seeking to access their emergency services on a daily basis," it said.

Intensifying fighting has left Taez in a desperate situation, with closed hospitals and acute shortages of medicine, food, water and fuel, the Red Cross said this week.

The Huthis overran Yemen's capital Sanaa in September 2014 and went on to seize control of several regions, aided by Saleh's forces.

In July, loyalists backed by the Saudi-led coalition evicted the rebels from five southern provinces and have set their sights on Sanaa.

At least 4,500 civilians have been killed in the conflict since March, when the coalition began targeting the rebels in air strikes.