Saudi forces on Sunday intercepted seven missiles fired by Yemen's Iran-backed Huthi rebels into Saudi Arabia, killing one person and wounding two others.

Guterres "strongly condemns the launch late yesterday of a series of missiles claimed by the Huthis toward cities in Saudi Arabia, including Riyadh, as he does consistently with all attacks against civilians," said a UN statement.

He called for "restraint amid mounting tensions and stresses that military escalation is not the solution."

The UN chief is due to meet Saudi Crown Prince Mohammed bin Salman at UN headquarters on Tuesday to discuss Yemen.

The United Nations is making a fresh push for talks after Iran sent signals that it would be willing to help turn up the pressure on the Huthis to take part in negotiations, UN diplomats said.

New UN envoy Martin Griffiths was in the rebel-held capital Sanaa this week for talks on kick-starting the political process, following a first round of meetings in Riyadh.

About 10,000 Yemenis have been killed and 53,000 wounded since the coalition intervened in Yemen in March 2015.

On Sunday, the Huthis fired three missiles at Riyadh and four others at the southern cities of Khamis Mushait, Jizan and Najran.

The Saudi-led coalition said the attacks all targeted populated areas.

The United Nations has said Yemen is facing the world's worst humanitarian crisis, with 22.2 million people in need of aid, a growing risk of famine and a severe outbreak of cholera.