According to Husi, Yemeni President Abd Rabbu Mansour Hadi and head of the Houthi political council, Saleh Sammad, have reached an agreement during a meeting earlier on Wednesday.
Meanwhile, government sources told Sputnik that Hadi had accepted four demands put forward by the Houthi opposition leader, Abdul Malik al-Houthi.
Reports on Tuesday indicated that Houthi fighters had stormed and seized the presidential palace in Sanaa, which the Arab States of the Gulf's (GCC) foreign ministers have referred to as a coup in a statement, issued after an emergency meeting later on Wednesday.
The Shiite Houthi are a major opposition force in Yemen that were involved in removing former Yemeni leader Ali Abdullah Saleh from office in 2012. In September 2014, the insurgency spread to the central and western parts of the country.