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 a ceasefire to try to de-escalate the conflict, Reuters reported.

Two of the sources said Saudi airstrikes 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 Mohammed 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.

A senior military source in Yemen on the Houthi side said that Saudi Arabia had “opened communication” with the head of the Houthi political office, Mahdi al-Mashat, via a third party, but no deal had been reached.

This offer involved a partial ceasefire in certain areas, the source said. Two diplomatic sources and the source familiar with the matter also said a partial ceasefire was on the table.

But Houthi officials have said a partial deal is unacceptable. “What is required is a complete cessation of airstrikes in all of Yemen and an end to the siege on the Yemeni people,” the Houthi information minister said.