Saudi Arabia is considering a proposal by Yemen’s Iran-aligned Houthi movement for some form of ceasefire which, if agreed, could bolster U.N. efforts to end a devastating war tarnishing Riyadh’s reputation.

The Houthis offered two weeks ago to stop aiming missile and drone attacks at Saudi Arabia if the western-backed coalition led by Riyadh does the same, as a step to what a Houthi leader called a “comprehensive national reconciliation”.

There was no immediate Saudi acceptance or rejection of the Houthi offer. But Riyadh this week welcomed the move, and three diplomatic and two other sources familiar with the matter told Reuters the kingdom is seriously considering some form of ceasefire to try to de-escalate the conflict.

Yemen’s 4-1/2-year-old war, which the United Nations has described as the world’s worst humanitarian disaster, has pushed what was already one of the poorest Arab states to the brink of famine.

U.N.-mediated efforts to resolve the complex war have been tortuous, with cross-border strikes by both sides a central grievance for the Houthis and Saudi Arabia, which borders Yemen.

Two of the sources said Saudi air strikes on Houthi territory had decreased significantly, and that there were reasons to be optimistic about some sort of deal emerging soon.

Saudi Arabia’s vice minister of defense, Prince Khalid bin Salman, said on Thursday on Twitter the kingdom viewed the Houthi truce offer “positively”, echoing comments earlier this week by Saudi Crown Prince and de-facto ruler Muhammad bin Salman, also known as MbS.

The Houthi proposal was a “positive step to push for more serious and active political dialogue ... Today we open all initiatives for a political solution in Yemen. We hope this happens today rather than tomorrow,” MbS said in a CBS television interview.Reuters