Shortly after he spoke, parliament voted 50 to one to reinstate Bakiyev's right to appoint the prime minister and government, as well as all regional governors.
Opposition deputies boycotted the vote.
Bakiyev, elected by a landslide last year after the previous Kyrgyz leader, Askar Akayev, fled amid a violent coup, also won back control over the army and security services.
After a wave of street protests staged by the opposition last month, the president signed a new constitution that would have cut his powers and given the legislature the ability to appoint a new government.
After the protests, Kyrgyzstan could have become the first state in authoritarian post-Soviet Central Asia where parliament has strong checks and balances on the president.
On Monday, however, deputies blocked an attempt to reinstate Bakiyev's powers, which angered the president and caused him to call parliament to vote on the matter.
Strategically located Kyrgyzstan, which hosts Russian and US military bases, has been without a formal government since Felix Kulov, the prime minister, resigned this month in response to the constitutional changes.