The U.N.-sponsored talks should resume "but only after a complete halt of attacks," Houthi spokesman Mohammed Abdulsalam said in a Facebook post.

The previous round of talks between Houthi rebels and the government of Yemeni President Abdu Rabu Mansour Hadi failed in January after rebels attacked the President's personal residence and presidential palace in Sanaa, the Yemeni capital.

On Tuesday, Saudi Arabia announced the end of its Operation Decisive Storm , a nearly monthlong air campaign against Houthi positions. The Saudi-led coalition said a new initiative was underway, Operation Renewal of Hope, focused on the political process.

But less than 24 hours later, after rebel forces attacked a Yemeni government military brigade, the airstrikes resumed, according to security sources in Taiz. Five airstrikes targeted a weapons depot in the province late Wednesday, two Taiz security officials said. Explosions lasted for about 40 minutes, they said.

It was unclear whether it was a resumption of the operation or a short-term series of strikes.

Meanwhile, Houthis released Yemeni Defense Minister Mahmoud al-Subaihi in Sanaa on Wednesday, according to a senior Saudi source speaking on condition of anonymity.

The Houthis had said they detained the defense minister at an air base near the Yemeni port city of Aden on March 26, shortly before the Saudis began their airstrike campaign. The rebels captured the base that day as part of an advance on the Aden area.

The United Nations demanded al-Subaihi's release earlier this month.

Saudis claim victory

Saudi Arabia and its coalition partners launched airstrikes on Houthi positions across Yemen starting on March 26, hoping to wipe out the Iranian-allied rebel group that overthrew the government and seized power.

The Saudis say they want to restore the Yemeni government -- a key U.S. ally in the fight against al Qaeda -- which was kicked out of the capital by the rebels earlier this year.

This month, Saudi officials said airstrikes have degraded Houthi-controlled military infrastructure, including key buildings in Sanaa.

The campaign achieved its objectives "by a very good planning, very precise execution, by the courage of our pilots, our sailors, our soldiers," said Brig. Gen. Ahmed Asiri, a Saudi military spokesman.

A senior Saudi official told CNN that the Houthis agreed to "nearly all demands" of the U.N. Security Council. Former Yemeni President Ali Abdullah Saleh and his family will leave Yemen and never return for a position in politics, the source said.

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A statement from the Saudi Embassy in Washington outlined objectives of the next phase of operations, including protecting civilians, enhancing humanitarian and medical assistance, confronting terrorism and creating an international coalition to provide maritime security.

Ground troops will continue to protect the border and confront any attempts to destabilize the situation, Asiri said. Military action will be taken if needed.

Political solution sought

But beyond the military campaign, the Saudis and their allies have said they want to find a political solution for the violence-plagued nation.

"Thank God they didn't kill us this time" Wigdan, 6, woke up to bullets & shrapnel near her bed. #Yemen @UNICEF_Yemen pic.twitter.com/FK5xZH6ct7 — UNICEF (@UNICEF) April 21, 2015

The aim is to bring back "security and stability through establishing a political process," said a statement from Saudi Arabia, the United Arab Emirates, Bahrain, Qatar and Kuwait.

Hadi, who claims he's Yemen's legitimate leader, thanked the Saudi-led coalition. He is working with the Saudis and other allies to return to his country.

"We promise to restructure the Yemen military to ensure that it serves the people of Yemen," Hadi said, calling on the Houthis to withdraw, and saying that he would return to Yemen at "the right time" to rebuild the country.

"You will witness many changes in the days to come in our mission to build an institutional government and military, far from rebel militancy," said Hadi.

Drone strikes continue

In the country's south, security officials on Wednesday reported two U.S. drone strikes against al Qaeda militants in Mukalla. Six suspected militants died in the attack.

This is the second drone strike in three days. On Monday, six militants were killed when drone strikes targeted two vehicles in Shabwah, west of Mukalla.

A U.S. military official told CNN on Tuesday that the United States is conducting "manned reconnaissance" off Yemen. The official stressed that the repositioning of U.S. ships over the last few days was not done to interdict Iranian ships, but to ensure freedom of navigation and maritime security.