UNITED NATIONS—Saudi Arabia and Houthi rebels agreed to a cease-fire in Yemen and a resumption of peace talks in April, raising hopes for an end to a conflict that has killed thousands of people and sparked a humanitarian crisis.

“The war in Yemen must be brought to an end before it does irreparable damage to the future of Yemen and the region,” said Ismail Ould Cheikh Ahmed, the U.N.’s special envoy for Yemen.

The cease-fire is set to begin April 10, with peace talks resuming the following week, he said.

The talks would focus on five areas: withdrawal of militia and armed groups, handover of heavy weapons to the state, arrangements for interim security, restoration of state institutions and creation of a special committee for prisoners and detainees.

The U.N. plan would enlist prominent Yemeni figures to form committees that would monitor the cessation of hostilities and record progress or security incidents. The U.N. has also asked both sides to present a concept paper on the five focus areas by April 3.

Diplomats welcomed the news and said the Security Council would be issuing a statement in the coming days voicing its support of the U.N.-brokered cease-fire and resumption of talks.

In September 2014, Houthis backed by Iran and former President Ali Abdullah Saleh took over the capital San’a and sent President Abed Rabbo Mansour Hadi into exile. Saudi Arabia, backed by the U.S. and a coalition of Arab allies, began airstrikes in March 2015 to help restore the government. Since then 6,000 people, half of them civilians, have been killed and more than 30,000 injured, the U.N. said.

Mr. Cheikh Ahmed said terrorist networks were expanding in Yemen, taking advantage of the power vacuum created in many parts of the country. Al Qaeda affiliates have thrived and seized large territory in south and east Yemen since the conflict began in September 2014. A branch of Islamic State has also targeted the government and Houthi rebels in lawless regions.

A Security Council diplomat said weeks of negotiations led to the agreement, focusing on direct negotiation between Saudi Arabia and Houthis at the border, political-level diplomacy and laying the groundwork for a Security Council action that would highlight the dire humanitarian situation.

“There can’t be a military solution to Yemen. It has to be a political solution,” said Matthew Rycroft, U.K. ambassador to the U.N.

A Saudi coalition spokesman said last week that combat operations in Yemen were nearing an end. Saudi Arabia and the Houthis recently agreed to a prisoner swap and a cessation of hostilities along the border between Saudi Arabia and Yemen, although the scope of the deal was limited.

Saudi Arabia has faced criticism for targeting civilians and public spaces such as markets, hospitals, clinics and schools. U.N. High Commissioner for Human Rights Zeid Ra’ad Al Hussein told the U.N. that targeting civilian structures occurred “with unacceptable regularity.”

Saudi Arabia’s mission to the U.N. said it wouldn’t comment on the cease-fire or the allegations of targeting civilians.

This week, Human Rights Watch and Amnesty International called for the U.S. and U.K., as well as other weapons suppliers, to refrain from selling and transferring arms to combatants in Yemen and to Saudi Arabia. The Human Rights Watch report called for an arms embargo against Saudi Arabia “until it not only curtails its unlawful airstrikes in Yemen but also credibly investigates alleged violations.”

—Asa Fitch in Dubai contributed to this article.