ADEN, Yemen — Ali Abdullah Saleh, the former president of Yemen, said on Saturday he was ready for a “new page” in ties with the Saudi-led coalition fighting in Yemen if it stopped attacks on his country, in a move that could pave the way to end nearly three years of war.

The apparent shift in position came as Mr. Saleh’s supporters battled Houthi fighters for a fourth day in the capital, Sanaa, in fighting which the International Committee of the Red Cross said has killed dozens of people.

The fighting was the most serious since the Houthis and Mr. Saleh’s General People’s Congress made common cause against the Saudi-led coalition, which joined the Yemen war in 2015 to try to restore the internationally recognized government of President Abd-Rabbu Mansour Hadi to power.

The clashes between Mr. Saleh’s supporters and the Houthis underscore the complex situation in Yemen, one of the poorest countries in the Middle East, where a proxy war between the Iran-aligned Houthis and the Saudi-backed Hadi has caused one of the worst humanitarian catastrophes in recent times.