Kulov and Bakiev are under fire over a purported security plot to frame opposition lawmaker Omurbek Tekebaev.
Tekebaev, who was briefly detained last week in Poland on drugs charges, claims the National Security Service (SNB) set him up. A Polish court ruled that the heroin found in Tekebaev's luggage had been planted.
Addressing parliament today, Kulov said his departure and that of Bakiev would be detrimental to the country's stability.
He also urged parliament to amend existing legislation so that the SNB is placed under the joint supervision of the government and the legislature.
The SNB currently reports directly to the president.
Bakiev today reportedly fired his brother Janysh from his post as first deputy chairman of the SNB.
Kyrgyz lawmakers on September 11 made public a letter in which the deputy head of Manas airport, Nadyr Mamyrov, suggested Janysh Bakiev had instructed him to hide drugs in Tekebaev's luggage prior to a visit to Poland.
Mamyrov said on September 12 that the letter was a fake and, and Janysh Bakiev denied instructing security officials at Bishkek's Manas airport to plant place the drugs in Tekebaev's luggage.