Washington (CNN) Peace talks to end the conflict in Yemen will take place in Sweden in the next few weeks, Secretary of Defense James Mattis said Wednesday, as experts cautioned that there's no guarantee Saudi Arabia will take the steps needed for that to happen.

The conflict of nearly four years between a coalition led by Saudi Arabia and Houthi rebels backed by Iran has killed around 57,000 people, according to the Armed Conflict Location & Event Data Project, a crisis mapping project. The UN has put the death toll at 10,000, but that estimate has not been updated for years, during which the country has edged to the brink of starvation, with 14 million lives at risk in what the UN describes as possibly the worst famine in 100 years.

The conflict, which began as a civil war after the ouster of a strongman leader, gathered force when Saudi Arabia and allies entered the war to counter what they saw as Iranian influence. The Gulf coalition received logistical and intelligence support from the US, UK and France, which have also been selling weapons to Saudi Arabia.

Mattis said that both the Houthi rebels and the internationally recognized government of President Abdrabbuh Mansour Hadi had agreed to attend.

'You need a major change'

"It looks like very, very early in December up in Sweden we'll see both the Houthi rebel side and the UN-recognized-President Hadi's government will be up there," Mattis told reporters at the Pentagon. "The Saudis and the Emiratis are fully on board," he added.

The defense secretary credited the United Nations Special Envoy on Yemen, Martin Griffiths, as well as Sweden, for helping to get the talks going.

The United Kingdom has also filed a draft resolution at the UN that emphasizes an end to hostilities and access for humanitarian aid. The draft calls for a two-week break in fighting to allow aid into the besieged country.

Aaron David Miller, a vice president at the Wilson Center, said President Donald Trump's statement of support for Saudi Crown Prince Mohammed bin Salman in the face of Washington Post journalist Jamal Khashoggi's murder suggests the US won't lean hard on Riyadh.

"You need a major change in Saudi policy to tamp down the violence in Yemen and yesterday's statements suggests to me we're not going to use the leverage we have," Miller told CNN. "We have massive leverage with the Saudis, but I see zero indication that Trump is prepared to weigh in heavily."

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Mattis spoke to reporters Wednesday not long after the international aid group Save the Children announced that between April 2015 and October 2018, about 85,000 children under the age of five starved to death in Yemen because of the Saudi coalition blockade of a central port, violence and other disruptions.

The announcement Wednesday came as intense fighting has again erupted in the strategic port city of Hodeidah, a vital entry point for UN and other humanitarian aid and the center of the conflict between the US-backed Saudi-led coalition and the Iranian-aligned Houthis.

On Wednesday, Mattis said that the Saudis and the Emirates have ceased offensive operations around Hodeidah. He said that while "there has been still fighting, I would characterize it probably as a reduced level."

Mattis and Secretary of State Mike Pompeo called for an end to the hostilities and for peace talks at the end of October. Pressure for the US to scale back its support for Saudi Arabia is growing following Democratic victories in the House in the midterm elections and is likely to intensify after Trump's statement on the Saudi crown prince and Khashoggi's murder.

'A tragedy'

Lawmakers are calling for the US to stop providing Saudi Arabia with logistical support in Yemen or selling it arms -- a push Trump strongly rejected in his statement and in remarks to reporters Tuesday.

Bruce Riedel, director of the Intelligence Project at the Brookings Institution, noted that Trump's statement undercut his administration's diplomatic efforts to end the Yemeni violence. Some officials had been using the Khashoggi murder as leverage to get the Saudis to end the war.

Now, Riedel noted, that leverage is off the table as Trump's statement basically absolved Saudi Arabia and laid the blame at Iran's feet. Personal dynamics could also play a factor in making it hard to pressure the Kingdom to end the war. Trump doesn't like to admit he's made a mistake, Riedel noted, and the prince's ego is wrapped up in achieving a positive outcome for Saudi Arabia in the conflict.

"Khashoggi's murder is a tragedy," Riedel said. "The Yemen war is much more than a tragedy. When do you take a stand on moral issues?"