The Central Asian country's leader accepted the government's request to resign en bloc earlier Tuesday amid the Cabinet's ongoing standoff with parliament.
Kulov said the standoff was due to the adoption of a new Constitution last month, which sets out a new method for forming the Cabinet.
He said ten lawmakers had submitted a letter to the president's administration and to parliament, calling the Cabinet and parliament illegitimate.
The new Constitution, signed after a week-long opposition-led rally in the capital, Bishkek, and based on a compromise agreement drafted by opposition and pro-government lawmakers, stipulates the Cabinet shall be formed by the party that wins parliamentary elections, and expands parliament to 90 deputies from the current 75.
Under the Constitution, the president lost the right to dissolve parliament, and parliament gained the authority to appoint the prime minister and the Cabinet.
Bakiyev came to power in March 2005 on the back of a "tulip revolution," which ousted the country's first president, Askar Akayev, but his rule has been marred by economic problems, high-profile murders, prison riots and disputes over the control of lucrative businesses.
Earlier Tuesday, Bakiyev dismissed the head of the country's Central Election Commission, Tuigunaaly Abdraimov, who had earlier tendered his resignation.
Experts predict a political crisis following the Cabinet's resignation. However, State Secretary Adakhan Madumarov said President Bakiyev and the prime minister would coordinate efforts to rectify the situation.
"The Kyrgyz president and the government are making coordinated efforts in one direction," he said. "We need to adjust everything in compliance with the new Constitution."