An Omani delegation has arrived in Yemen's rebel-held capital to discuss extending a nationwide ceasefire that expires on Tuesday, Houthi media reported on Sunday.

The UN-brokered truce that went into effect on April 2 was extended for another two months in June. It has provided a window of relative calm after seven years of civil war and has been seen as an opportunity for the warring sides to reach a political agreement to end the conflict.

delegation's visit coincided with UN envoy Hans Grundberg's meeting with the Houthis in Sanaa, after talks with the government now based in the southern city of Aden.

Mr Grundberg has suggested that a third extension of the truce could be for a longer period than two months.

The UN and the US have intensified efforts to extend the truce despite some of its terms not being met, in particular the reopening of roads around the rebel-besieged city of Taez.

US Secretary of State Antony Blinken spoke by phone to the head of Yemen's presidential council, Rashad Al Alimi, on Sunday, a day after speaking to Oman's Foreign Minister Sayyid Badr Al Busaidi, about the importance of renewing the truce.

Mr Blinken described the ceasefire as Yemen's "best opportunity for peace in years".

Mr Al Alimi highlighted to Mr Blinken the "failed experiments of appeasing Houthi militia, and most recently the UN truce," state news agency Saba reported.

"The Houthi militia relinquished all its commitments included in the truce, including its continuous siege on Taez and other provinces," Saba quoted him as saying.

The government's demand for the Houthis to reopen the roads around Taez, Yemen's third-largest city, remains one of the biggest sticking points for extending the truce. Mr Al Alimi refused to meet Mr Grundberg in Aden because of his anger over the issue, sources said last week.

Despite a significant reduction in violence, both sides accuse each other of violating the truce. Most recently, the Houthis conducted an attack in Taez that killed a child and wounded 11 others. The Armed Conflict Location and Event Data Project has recorded 1,173 "shelling, artillery or missile attacks" since April 2, but no air strikes.

It also said 228 drone strikes have taken place since April 2.