RIYADH, June 2 (Reuters) - Yemen's warring parties agreed to extend a U.N.-brokered truce for another two months under the same terms as the original deal that was due to expire on Thursday, the U.N. envoy to Yemen said.

Delegations from the Saudi-backed government and the Iran-aligned Houthi movement are expected to return to the Jordanian capital Amman to continue talks, a Yemeni official said.

The truce that began on April 2 saw a halt to major military operations in Yemen and cross-border attacks in the seven-year war between a Saudi-led coalition and the Houthi group, and helped ease a humanitarian crisis that has left millions hungry.

The truce is the most significant step in years towards ending the conflict that has killed tens of thousands of people and added tensions to an already strained relationship between Riyadh and Washington.

"For the past two months, Yemenis have experienced the tangible benefits of the truce," United Nations Special Envoy for Yemen Hans Grundberg said in a statement.

U.S. President Joe Biden welcomed the truce's extension and said it would not have been possible without regional diplomacy.

The renewed agreement will allow for fuel ships to continue to dock into Houthi-held Hodeidah port and some commercial flights from the airport in the capital Sanaa, which is controlled by the group.