Bakiyev condemned the proposed protests, and said that "we will take the toughest measures to stop any illegal actions and punish those responsible".
Bakiyev became acting president in 2005, after street demonstrations drove Askar Akayev, then president, from office.
He was later elected president in voting that was assessed to be the most free and fair in ex-Soviet Central Asia, but since then his time in office has been plagued by allegations of cronyism and corruption.
Bakiyev has been under growing pressure since December, when he reversed several constitutional amendments and reinstated presidential authority to form the cabinet.
Under the most recent amendments, though, parliament would appoint the prime minister and propose members of the cabinet.
In recent weeks Bakiyev has made several concessions to the opposition, including the appointment of Almaz Atambayev, an opposition leader, as prime minister.
"As president, I have done everything I could," Bakiyev said on Tuesday. "In response, I only hear ultimatums and reluctance to negotiate."
The constitutional changes must be approved by parliament.
Atambayev said legislators might begin discussions on Wednesday.
"These changes will give us a strong parliament, strong government, strong judicial branch and strong president," Atambayev told a news conference.
It was not clear how much support Wednesday's demonstration would attract, but up to 100 demonstrators have been camped outside parliament on hunger strike in traditional felt tents, known as yurts, since Thursday.
The prospect of protests that could bring new instability to Kyrgyzstan is a concern to the US and Russia, which have interests in the country.