Kulov told reporters:"By our move we are trying to speed up new parliamentary elections. This is a way out of a crisis and a way to intensify the democratic process."
Last month, after a week of increasingly angry opposition protests which were supported by parliament, Bakiyev was forced to sign constitutional amendments curtailing his powers and giving broader authority to parliament and the cabinet.
Kulov's deputy, Daniyar Usenov, said that the adoption of the new constitution was "a mistake" and made it impossible for the cabinet to work with parliament.
"Bakiyev must accept our resignation and he has the right to call new elections ... a new parliament needs to be elected so we can advance our reforms," Kulov said.
Bakiyev came to power in March 2005 following opposition protests that removed ruler Askar Akayev.
He subsequently won an election but his rule has been marred by corruption, lawlessness and a weak economy.
Bakiyev has had a troubled relationship with parliament, which accused him of delaying his election promise to give broader powers to lawmakers.
Lawmakers were gathering for an emergency meeting Tuesday afternoon.
Omurbek Tekebayev, an opposition lawmaker, told The Associated Press that the cabinet's resignation was "unexpected" and "perhaps connected with plans to reform government," but declined to comment on calls to dissolve parliament.
The impoverished, mountainous country of 5 million people is strategically located near China and Afghanistan and has been seen as an example of secular democracy in a region dominated by autocratic regimes and Islamic militants.