Pressure has mounted on warring parties to end war that killed thousands and pushed the country to the brink of famine.

A senior leader from Yemen’s Houthi rebels says his group will halt all rocket and drone attacks on Saudi Arabia and the United Arab Emirates (UAE) and is ready to institute a ceasefire – if the Saudi-UAE alliance battling his movement is prepared to do the same.

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

Al-Houthi called on the group’s forces to refrain from carrying out attacks and said that, in a gesture of goodwill, the movement would halt all missile and drone attacks on Saudi Arabia, the UAE and their Yemeni allies.

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“We announce our initiative and call on the official Yemeni [Houthi] authorities to stop firing missiles and unmanned aircraft at the US-Saudi aggression countries and their allies in Yemen to drop any justification for their continued aggression or siege,” he added.

International pressure has mounted on Yemen’s warring parties to end the war, which has killed more than 56,000 people, according to a recent estimate, and pushed the country to the brink of famine.

On Monday, the United Kingdom is expected to present a draft resolution to the Security Council to address the conflict.

We want to prove to the world that we want peace Mohammed al-Bukhaiti, member of the Houthis' political bureau

‘Major relief for Yemenis’

UN Special Envoy Martin Griffiths has been trying to broker peace talks and is expected to travel to Sanaa this week and meet with the group’s leader, Abdul Malik al-Houthi.

He will also travel to Hodeidah to discuss plans for the United Nations to take control of the city’s port and oversee the arrival of aid deliveries and supplies.

The rebel-held port is the main entry point for humanitarian aid and goods and before the war, it accounted for 70 to 80 percent of the nation’s vital imports.

Last week, pro-government forces suspended an offensive to retake the port following days of incessant air raids.

Griffiths said the warring sides had given him “firm assurances” they were committed to attending peace talks, which are expected to be held in Sweden before the end of the year.

Saudi Arabia and the UAE both have said they support UN-led peace talks.

Al Jazeera’s Mohammed Adow, reporting from neighbouring Djibouti, said the Houthi announcement was a “big deal” for the millions of Yemenis staring at famine.

“The Houthis said they made this decision following a request from Griffiths.

“It will come as a major relief for the hundreds of thousands of civilians still trapped in Hodeidah who have been bracing themselves for further conflict.”

Deadly air raids

The Houthis say their missile attacks on Saudi Arabia and the UAE are in retaliation for the thousands of air raids they have carried out on Yemen since they entered the war in March 2015.

The conflict in Yemen began nearly a year earlier when the Yemeni government slashed fuel subsidies in the summer of 2014, prompting massive protests in Sanaa.

The Houthis seized on the opportunity and marched south from their stronghold of Saada province to the capital, where they toppled President Abd-Rabbu Mansour Hadi’s government.

Accusing the Houthis of being Iranian proxies, the alliance launched a massive aerial campaign aimed at rolling back their advances.

Since then, the alliance has carried out more than 18,000 air raids, with nearly a third hitting civilian targets such as schools, markets and hospitals, according to the Yemen Data Project, an independent watchdog.

Mohammed al-Bukhaiti, a member of the Houthis’ political bureau, said the group wanted to “prove to the world” that it “wants peace.”

“When Saudi Arabia started its aggression against Yemen [in March 2015] we did not respond for 40 days. We wanted to show who is doing what. We wanted to make sure that Saudi Arabia cannot find justifications if we respond.

“Today’s step aims to once again clarify our position. We also announced that we are ready to stop all operations at all fronts to show the world who is doing what and to give peace a chance. We want to prove to the world that we want peace.”