A prisoner swap between the Houthis and the internationally recognized, Saudi-backed government of Yemen was one of three pillars of a breakthrough deal reached in December in Sweden.
The U.N.-brokered prisoner swap deal involving some 7,000 detainees on each side stalled as the two sides struggled to agree at talks on its implementation.
"Our initiative proves our credibility in implementing the Sweden agreement and we call on the other party to take a comparable step," said the head of the Houthis' prisoner affairs committee, Abdul Qader al-Murtada, in statements carried by Houthi-run al-Masirah TV.
"The 350 prisoners ... are included in the prisoner lists of the Sweden deal," he said.
A Saudi-led Sunni Muslim coalition, which receives arms and intelligence from Western countries, intervened in Yemen in March 2015 after the Houthis ousted the Yemeni government from power in the capital Sanaa in 2014.
The Houthis, who control most major urban areas, said on Sept. 20 they would halt missile and drone attacks on Saudi Arabia if the alliance stopped its operations. The coalition has not yet responded to the proposal.