Omar Humeidan said that the decision was made in a Sunday session of parliament by "consensus."
A law governing the new elections should be presented by next month, he added.
Parliament's term expired on February 7, but lawmakers voted to extend it without holding new elections. Since then, crowds have been protesting to demand parliament be dissolved.
The country marks Monday the anniversary of the start of the 2011 revolt that brought down longtime dictator Moammar Gadhafi.
The anniversary comes as Libya's new rulers battle critics calling for a "new revolution" and accusing them of failing to usher in much-needed reforms.
RA/NJF