(This story corrects origin of report as source, not negotiator)

DUBAI/SANAA (Reuters) - A senior U.S. diplomat has presented a proposal for a comprehensive ceasefire in Yemen to the country’s dominant Houthis at a meeting in Oman, a source close to the Houthi negotiating team said on Thursday.

Negotiators will return to Houthi-controled Sanaa on Friday carrying the plan offered by U.S. Undersecretary of State for Political Affairs Thomas Shannon in talks in Muscat, the source said.

Shannon met the Houthi team, officials of the allied General People’s Congress (GPC) party and an Omani mediator in Muscat on Sept. 8 and 9 to discuss how to end a war that has killed over 10,000 people and displaced more than 3 million.

In Washington, U.S. officials said the plan was an “extension of the efforts Secretary (of State John) Kerry initiated in Jeddah.”

The source did not disclose details of the proposal. Kerry said in Saudi Arabia on Aug. 25 he had agreed in talks with Gulf Arab states and the United Nations on a plan to restart peace talks on Yemen with a goal of forming a unity government.

Yemen’s crisis began in September 2014 when the Iran-allied Houthis seized the capital, Sanaa. A Saudi-led Arab alliance intervened in support of the country’s internationally recognized government led by President Abd-Rabbu Mansour Hadi. U.N.-sponsored negotiations to end the fighting collapsed last month.

Peace talks foundered after the Houthis and the GPC announced the formation of a 10-member governing council on Aug 6., ignoring a U.N. warning that such a move would violate Security Council resolutions on how to solve the conflict.

The Houthi negotiating team has been in Oman since the collapse of the peace talks, after Saudi authorities in control of Yemen’s airspace refused to grant the Houthi team access to Sanaa, the source added.

Saudi authorities have now agreed to allow the negotiating team to return to Yemen in a U.N. airplane, the source said.

In a statement on the Kerry proposal on Thursday, the governing council reiterated that its willingness to restart peace talks depended on implementation of a full ceasefire, including the lifting of the no-fly zone and siege imposed by the Saudi-led coalition.

Forces allied to the Houthis attacked across the border into Saudi Arabia’s southern Jizan province on Thursday, with both sides claiming victory and giving conflicting casualty tolls.

Sources in the Saudi-led coalition said Saudi forces at the Jabal Dukhan mountain repelled the attack by Yemeni Republican Guard troops loyal to former President Ali Abdullah Saleh, killing about 25 and wounding 30.

In the Yemeni capital, Sanaa, a Houthi official said the clash resulted in the Houthi capture of the mountain as well as a place called Al Romaih. The commander of a Saudi rapid intervention force was killed in the fighting, he added.