The Council was created by Houthi rebels and their ally, ex-vice president Ali Abdullah Saleh, at the end of July to govern the country, Efe news reported.
More than 900,000 Yemenis gathered in Sana'a with flags and pictures of the newly-elected Political Council leader Saleh al-Sammad to show their support on Saturday.
"The formation of a government is intended to unify our efforts to stabilize the situation and hold general elections," said al-Samad in a speech to the crowd.
Saudi Arabian-led coalition bombers performed four air strikes 300 meters (328 yards) away from where the march took place, killing three Houthi fighters and injuring another three.
Yemen has been gripped by civil war since 2015, as the Shia-led Houthi movement and the predominantly Sunni forces loyal to beleaguered President Abd Rabbuh Mansur Hadi fight for power in the country.
