(CNN) Rebels in Yemen announced Sunday that they would stop missile and drone strikes on Saudi coalition targets at the request of the United Nations.

The development comes as Riyadh faces growing pressure to put a halt to the violence in Yemen after three-plus years of devastating war.

"We are willing to freeze and stop military operations on all fronts to reach a just and honorable peace if they really want peace for the Yemeni people," Mohammed Ali al-Houthi, head of Yemen's Houthi Supreme Revolutionary Committee, said in a statement.

Al-Houthi also said his forces would stop launching missiles and drone attacks on "US-Saudi aggression countries and their allies in Yemen," an apparent reference to Saudi Arabia and its coalition partner, the United Arab Emirates.

The United States has backed the Saudi-led coalition in its fight to expel Iranian-aligned Houthi rebels from Yemen, but has in recent weeks called for an end to the coalition bombing campaign in the country.

In a gesture of goodwill, al-Houthi called on Houthi forces to refrain from attacks.

"We announce our initiative and call on the official Yemeni (Houthi) authorities to stop the firing of missiles and unmanned aircrafts on the US-Saudi aggression countries and their allies in Yemen to drop any justification for their continued aggression or siege," he said.

On October 30, US Secretary of Defense James Mattis and the US State Department called on the participants in the conflict in Yemen to agree to a ceasefire "in the next 30 days."

"Thirty days from now we want to see everybody around a peace table based on a ceasefire, based on a pullback from the border and then based on ceasing dropping of bombs that will permit the (UN) special envoy, Martin Griffiths -- he's very good, he knows what he's doing -- to get them together in Sweden and end this war," Mattis said at an event at the US Institute of Peace in Washington.

His call was later echoed by Secretary of State Mike Pompeo, who issued a statement saying, "The United States calls on all parties to support UN Special Envoy Martin Griffiths in finding a peaceful solution to the conflict in Yemen."

"Substantive consultations under the UN Special Envoy must commence this November in a third country," Pompeo added.

Mattis said the talks should lead to the implementation of "confidence-building measures to address the underlying issues of the conflict, the demilitarization of borders and the concentration of all large weapons under international observation."

Activists and some members of Congress have criticized the Trump administration for its support for the Saudi-led coalition fighting the Houthis in Yemen, and for the administration's recent finding that the coalition wasn't doing enough to avoid civilian casualties.

Earlier this month, the US announced that it would no longer refuel Saudi aircraft conducting strike missions over Yemen. The move was expected to have minimal impact on the Saudi effort because the US was only providing refueling for some 20% of Saudi aircraft.

The US military also provides the Saudi coalition with training meant to help minimize civilian casualties, as well as with intelligence to help guard against Houthi cross-border missile and drone attacks.

Last week, the Saudi-led coalition agreed to the evacuation of wounded Houthi fighters from Yemen, the British Foreign Office said, hailing it as a breakthrough toward getting a new round of peace talks. The announcement was made following a visit by Foreign Secretary Jeremy Hunt to Saudi Arabia and the UAE to discuss the ongoing conflict.

Sources: Saudi prince 'threw fit' over resolution

But multiple sources told CNN that a much-anticipated UN Security Council resolution calling for a cessation of hostilities to allow humanitarian aid to reach millions of starving people was "stalled" after Hunt's face-to-face meeting with Saudi Crown Prince Mohammed bin Salman.

Sources say Hunt took the draft with him to Riyadh and discussed it with the Crown Prince -- known in diplomatic circles by his initials, MBS -- who wanted changes or, better yet, no resolution at all.

Hunt left with the understanding that he would work on changes to the resolution with his team, as well as with his counterparts in the US and elsewhere. These allies share concerns that a bad reaction from Saudi Arabia to a strongly worded UN resolution could set back the start of a process to resolve the war in Yemen.

Even so, one of the sources familiar with the Riyadh meeting said Western allies "are not inclined to act on all of MBS's recommendations."

At a Security Council meeting Friday, British Ambassador Karen Pierce said the UK would introduce the new resolution on Monday.

The Department of State and Saudi Arabian Embassy in the US did not respond to requests for comment.

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David Miliband, the president and CEO of the International Rescue Committee, had called Pompeo's statement "the most significant breakthrough in the war in Yemen for four years."

"It is vital that this call for a ceasefire is followed through, and the call for support for the political process heeded," Miliband added.

After initially stepping up operations earlier this month, the Saudi coalition said Thursday that it had paused its offensive in the strategic port city of Hodeidah that day, due to international pressure. But it's unclear how long the lull will last. Turki al-Malki, a spokesman for the Saudi-led coalition, said last week that its military operations "are ongoing" and that "each operation has its own specifics and pace."

Griffiths, the UN's special envoy for Yemen, welcomed the reports of reduced violence Friday when addressing the UN Security Council. He said the two sides were about to finalize an agreement on the exchange of prisoners and detainees.