ADEN (Reuters) - Yemen’s warring parties suggested on Thursday that they would attend U.N.-sponsored peace talks expected to be held in Sweden next week as Western countries press for an end to a conflict that has pushed millions to the edge of starvation.

The United Nations is trying to reconvene talks between the Saudi-backed government led by Abd-Rabbu Mansour Hadi and the Iranian-aligned Houthis who control much of the north to agree on a framework for peace.

A previous attempt to hold talks in Geneva in September collapsed when the Houthis failed to show up, accusing their adversaries of obstruction.

Mohammed Ali al-Houthi, head of the Houthis’ Supreme Revolutionary Committee, said their delegation would arrive in Sweden on Dec. 3 “if safe exit and return is guaranteed and there are positive indications peace is a priority”.

Saudi-owned Al Arabiya TV said that Hadi’s delegation would arrive after the Houthis.

Outrage over the murder of Saudi journalist Jamal Khashoggi in the Saudi consulate in Istanbul has increased scrutiny of Riyadh’s activities in the region, potentially giving Western powers, which provide arms and intelligence to the Saudi-led military coalition trying to restore Hadi to power, greater leverage to demand action.

A spokeswoman for U.N. special envoy Martin Griffiths’ office declined to give a date for the talks but Michael Aron, Riyadh-based British ambassador to Yemen, tweeted to Houthi spokesman Mohammed Abdusalam that “the Sweden consultations led by the U.N. envoy will take place next week”.

Griffiths met representatives of Yemen’s political parties in Jordan. Two of them said Griffiths hoped to hold peace talks on Dec. 4, but that it would depend on the evacuation of 50 wounded Houthis. Griffiths said this would happen by Monday.

The attempt to convene talks in September collapsed after the Houthis asked for guarantees that their plane would not be inspected. They also wanted to evacuate some wounded to Oman.

British foreign minister Jeremy Hunt has said Saudi Arabia is willing to evacuate the wounded Houthis. Kuwait has offered to provide planes to get both sides to Stockholm.

The United Nations hopes to halt fighting around Hodeidah, the entry point for most of Yemen’s commercial imports and vital aid supplies, as a stepping stone to a broader ceasefire.

The Saudi-led coalition renewed its offensive to capture the port this month; the United Nations fears that an all-out attack could lead to a famine in Yemen, where an estimated 8.4 million people are threatened with starvation.

The Houthis have agreed to hand over the management of the port itself to the United Nations, but the warring sides are at odds over who should control the city.

The United Nations has no up-to-date estimate of the death toll in Yemen. It said in August 2016 that, according to medical centers, at least 10,000 people had been killed in the conflict.