HUDAIDA/ADEN, Yemen: Yemen’s Houthi group said Wednesday it was ready to stop fighting and join a national unity government, raising hopes of a resolution to a conflict that has killed more than 10,000 people. The announcement appeared to confirm the details of a deal set out by U.S. Secretary of State John Kerry a day earlier that he said included plans for a cease-fire starting Thursday.

Mohammed al-Bukhaiti, a member of the political council of the Houthi’s Ansarullah group, said Saudi Arabia had also agreed to end its involvement in the war – though there was no official confirmation from Riyadh.

An Arab alliance intervened in the Yemen conflict in March last year in support of President Abed-Rabbou Mansour Hadi after the Iran-aligned Houthis advanced on his interim capital in Aden and forced him into exile.

“Ansarullah’s position has been and still is with stopping the war and the establishment of a national unity government that incorporates all political components,” Bukhaiti told Reuters, responding to a question on Kerry’s announcement.

“The new thing is in the position of Saudi [Arabia], which has agreed in principle to stop the war as one of the parties to the conflict,” he added.

After months of bombings and other attacks, no side has emerged as the dominant force in a war that has displaced more than 3 million people, left parts of the population on the edge of starvation and given room for a powerful branch of Al-Qaeda to expand its operations.

Kerry, in what could be his last trip to the Gulf before President Barack Obama’s term ends in January, said Tuesday that officials from the Houthi group and the Arab coalition meeting had agreed to a cease-fire starting Thursday.

Underlining the complexity of the situation, Hadi’s government quickly rejected the move, complaining that it had been bypassed. Copies of a U.N. peace plan seen by Reuters in October suggested he would be sidelined in any future government.

Yemeni Foreign Minister Abdel-Malek al-Mekhlafi said Kerry’s announcement had not been coordinated with the government that, he said, was not interested in the plan.

Since Kerry’s announcement fighting on the ground has only intensified. Heavy clashes between government forces and rebels in north and west Yemen has left 51 dead, military officials said Wednesday.

They said forces loyal to Hadi have clashed since Tuesday with Shiite Houthi rebels and allied renegade troops in the country’s northwest, near the border with Saudi Arabia.

The fighting began as loyalists launched an attack on three fronts to recapture the coastal town of Midi and nearby Haradh, the officials said, adding that 15 loyalists and 23 rebels were killed in the fighting, the officials said.

“Our military operations will continue until we push them out,” said army Col. Abdul-Ghani al-Shubaili, whose forces had air support from the Arab coalition.

Elsewhere, nine rebels and four soldiers were killed in fighting on the outskirts of the city of Taiz, in southwest Yemen, military officials said.

Pro-Hadi forces have advanced toward the city’s presidential residence and police headquarters, both under rebel control, witnesses said, reporting heavy fighting and loud explosions that shook the city.

Fighting in Taiz and its surroundings Tuesday killed 39 people, including five civilians, 20 soldiers and 14 rebels, military officials said.