Yemen's Houthi fighters have been accused of breaking the country's humanitarian ceasefire in its first 24 hours, as fighting continued between rival sides in several parts of the country.

"The Houthi militias have violated the truce," the Arab coalition led by Saudi Arabia said in a statement on Thursday carried by the official Saudi Press Agency.

The statement alleged 12 breaches of the ceasefire, along the Saudi-Yemen border and in Yemen itself.

The heaviest violence on the ground was in the southwestern province of Taiz, where the Houthis and their allies - forces loyal to ousted President Ali Abdullah Saleh - shelled residential areas.

Fighting was also reported in the southern city of Ad-Dali', as rebels fired tank shells, rockets and mortars against positions belonging to forces loyal to exiled President Abd-Rabbu Mansour Hadi.

In the port city of Aden, coalition warships deployed off the coast shelled the rebels in an area that is home to fuel tanks.

Meanwhile, a Saudi defence ministry statement also accused the Houthis of violating the ceasefire by firing towards the Saudi border areas of Jizan and Najran.

It said the kingdom's armed forces were exercising restraint as part of their commitment to the ceasefire.

The Houthis had indicated they would abide by the ceasefire, which was proposed by Saudi Arabia and backed by the US in order to allow aid into the stricken country where the UN's food agency on Wednesday described the situation as "catastrophic".

As aid agencies said they were starting to deliver assistance, residents of the capital, Sanaa, said the ceasefire came as a much-needed relief.

More than 1,500 people have been killed since mid-March in the air campaign and fighting between the Houthis and Hadi loyalists, according to the UN.

The Houthi fighters, allied with army units loyal to former president Saleh, have taken control of large parts of Yemen, including Sanaa, and were advancing on Hadi's southern stronghold of Aden when the coalition launched the campaign. Hadi has since fled to Saudi Arabia.

In a separate development, the new UN envoy to Yemen, Ismail Ould Cheikh Ahmed, met with leaders of Saleh's one-time ruling party, the General People's Congress (GPC).

Ahmed said he intends to meet with Yemen's political leaders separately before talks bring them together to chart a political blueprint for Yemen.