DUBAI, DApril 2 (AFP) - The UN said Yemen's warring parties have agreed to a two-month extendable truce starting Saturday, the first day of Ramadan for many Muslims, and an accord on fuel shipments and Sanaa airport.

Friday's announcement brings a glimmer of hope in a brutal conflict that has killed hundreds of thousands and left millions on the brink of famine in Yemen, long the Arab world's poorest country.

"The parties to the conflict have responded positively to a United Nations proposal for a two-month truce which comes into effect tomorrow 2 April at 1900hrs," UN special envoy for Yemen Hans Grundberg said in a statement.

"The truce can be renewed beyond the two-month period with the consent of the parties."

UN chief Antonio Guterres welcomed the announcement, expressing hope for a "political process" to bring peace to the country.

"You must take that momentum in order to make sure that this truce is fully respected and that it is renewed and... that a true political process is launched," he said.

"This demonstrates that even when things look impossible, when there is the will to compromise, peace becomes possible," Guterres added.

The announcement comes as discussions on Yemen's devastating conflict take place in Saudi Arabia.

Riyadh has been leading a military coalition to support the government against the Iran-backed Huthis since March 2015, after the rebels seized the capital Sanaa the year before.

The Huthis, who rejected joining talks held on enemy territory, last week made a surprise offer of a temporary truce and a prisoner swap.

The coalition later said it would cease military operations in Yemen during the Muslim holy month of Ramadan.