The UN envoy for Yemen, called on Sunday, for an extension of the ceasefire, as a truce just ended with air strikes and ground fighting raging in the Middle East country.

Ismail Ould Cheikh Ahmed, urged all parties to extend the truce at least for another 72 hours, to create conditions for reviving stalled peace talks and reaching a permanent ceasefire.

"The Yemeni people deserve to live in peace and get all their fundamental rights and all parties should bear responsibility to protect them," he said.

The current 72-hour truce expired at 23:59 local time (2059 GMT) Saturday.

"Despite reported violations from all parties, since the truce took effect midnight last Wednesday, relief aid reached the affected areas and UN employees were able to move better in those areas, which previously were inaccessible," Ould Cheikh said, in a press release, hours after the truce expired.

The just-ended three-day truce began on Wednesday midnight, between the dominant Shiite Houthi rebels and exiled government of internationally recognised President Abd-Rabbu Mansour Hadi, backed by Saudi Arabia-led military coalition.

Houthis and their foes in the Hadi government traded accusations of breaching the truce in their media, as ground fighting raged, on largely all combat fronts throughout the days of truce.

Each side claimed their forces were repelling the other's attempts to advance towards their sites, on fronts of several Yemeni cities and provinces.

Saudi Arabia, which backs the Hadi government, accused Houthi fighters of firing rockets into its border cities of Jazan and Najran, killing two civilians. Houthis said, they retaliated Saudi-led air strikes on Saada province that they said killed several civilians.

The latest truce collapsed, after a series of attempts that also failed to cease the hostilities in Yemen since 2014. The previous fragile truce began in Apr, and ended last Aug, after the peace talks hosted by Kuwait yielded no breakthrough.

The conflict in Yemen began after the 2011 Arab-spring style mass protests eventually forced former President Ali Abdullah Saleh to step down.

The Houthis, supported by Saleh, seized the Yemeni capital Sanaa and some other Yemeni cities in Sept, 2014, forcing Hadi and his government into exile.

The Houthis and their ally forces loyal to Saleh have controlled most of Yemen's northern regions since then, while the Hadi government and its tribal allies have entrenched the southern provinces they recaptured from the Houthi rebels.

The Saudi-led coalition began to intervene in Yemen's conflict in Mar, 2015, with an air force campaign to restore Hadi to power and roll back Houthi gains.

The 19-month civil war in Yemen has killed more than 10,000 people, mostly civilians.