With global attention on Yemen focused on a fragile truce in its main port of Hodeidah, fighting between rival forces in the country's four-year war has surged elsewhere.

A Yemeni staff member of Action Against Hunger was killed by shrapnel on the roof of her home in the embattled city of Hodeida, the aid group said Tuesday.

Nine civilians were killed and at least 13 wounded earlier this week in attacks in the provinces of Hodeidah and Hajjah in war-torn Yemen, the UN said on Friday.

The UN special envoy to Yemen on Monday said the urgency of accessing grain stores trapped in a frontline position in the port city of Hodeidah was increasing as the food was "at risk of rotting".

The UN envoy for Yemen said Monday the expected timeline for a truce in the flashpoint city of Hodeidah and a prisoner swap between warring parties had been pushed back.

Yemen's warring parties have failed to pull troops from the main port under a month-old truce, putting the first major diplomatic breakthrough of the four-year war in jeopardy and reviving the threat of an all-out assault that could unleash famine.

A second round of negotiations between Yemen's government and Houthi rebels could be hosted "soon" in Jordanian capital Amman, a rebel leader said Sunday after meeting the UN envoy.

The UN envoy for Yemen arrived in the capital Sanaa on Saturday for talks to shore up a ceasefire in the country's lifeline port city of Hodeidah, an AFP photographer said.

Yemeni rebels have begun to withdraw from the port of Hodeidah, the country's key aid lifeline, under an agreement reached in Sweden earlier this month, a UN official said Saturday.

The head of the United Nations team tasked with monitoring a fragile ceasefire in the flashpoint city of Hodeidah on Monday visited its lifeline docks, a port official said.

Yemen's flashpoint city of Hodeidah was calm on Tuesday following heavy clashes that erupted after the UN-brokered ceasefire started at midnight, pro-government sources and residents said.

Air strikes and fierce clashes shook the outskirts of Yemen's rebel-held port city of Hodeidah overnight, pro-government sources and residents said Sunday, despite a UN-brokered ceasefire.