"The unilateral halt in naval military operations will be for a limited time period and could be extended and include all fronts if this move is reciprocated by the leadership of the [Saudi-led] coalition", SRC head Mohammed Ali al-Houthi said. Turki al-Malki said Thursday in a television interview.
The Saudi-led coalition backing Yemeni's internationally recognised government has been fighting to defeat the rebels, known as Houthis, since March 2015. "I saw people running and bodies in the street".
Martin Griffiths, Special Envoy for Yemen, has announced that peace talks will convene in Geneva starting on 6 September.
Yemen's civil war began in 2014.
He highlighted that "these consultations will provide the opportunity for the parties, among other things, to discuss the framework for negotiations, to agree on relevant confidence-building measures, and specific plans for moving the process forward".
A coalition spokesman did not immediately respond to a request for comment.
Mr Bin Mubarak said the council need to take a firm stand on the Houthi rebels retaining access to strategic areas from which they were launching attacks on global shipping.
However, Saudi Arabia claimed that Houthi fighters had attacked two oil tankers in the Red Sea, and thus it had made a decision to halt oil shipments via Bab el-Mandeb until the waterway was safe.
This came a few days after Saudi Arabia suspended oil exports through a strategic Red Sea channel, amid Houthi attacks on crude tankers on 25 July.
Launched in June by the House of Saud regime and the United Arab Emirates, the Hudaydah offensive is the largest battle in the Saudi regime-led war, which Yemeni officials say has killed and injured over 600,000 people.
The campaign to take the city threatens to worsen Yemen's humanitarian situation as it is the main entry point for food, humanitarian aid and fuel supplies to the country.
Yemen has become the "worst humanitarian crisis in the world", the European Union said, demanding the protection of civilians who continue to die in the three-year-old conflict.
As recriminations over Thursday's attacks escalated, the Saudis and their military partners in the Yemen conflict denied any responsibility and blamed their enemies, the Houthis, the Yemeni insurgent group that controls the seaport, Al Hudaydah.
Yemen is likely to be struck by another "major wave" of cholera cases, the World Health Organization said Friday, as it called for a three-day truce to allow vaccinations.