Parliament voted 39-23 on Thursday against reinstating Kulov.
After Kulov's move, Bakiyev threatened to dissolve Parliament and pushed through new amendments that restored his powers.
The assembly is likely to hold a new vote next week on whether to reappointing Kulov and his government.
Political instability
Kyrgyzstan has lurched from one political crisis to another since former president Askar Akayev fled violent protests in March 2005.
Bakiyev's critics accuse him of doing too little to root out corruption and poverty since his election.
The US maintains a military base in Kyrgyzstan - the only such outpost in former Soviet Central Asia - to support its operations in Afghanistan.
Russia, which has strong influence on Kyrgyzstan, also has an air base in the country.