A televised statement said the group was forming a presidential council that would run the country. It called the takeover "a new era that will take Yemen to safe shores."
The resignations compound a political crisis that began earlier this week when Shiite Houthi rebels took control of much of the capital, Sanaa, and surrounded the president's residence.
The agreement, which would see the rebels withdraw from parts of the capital in exchange for concessions, could defuse a political crisis that has threatened the stability of a key U.S. ally.