Kulov told journalists that he could not "just stay an observer" and said he was re-entering politics after resigning last year.
He said: "I have decided to ... unite and head all the fragmented but friendly political forces, all those who want radical and positive change."
The protests in November last year folowed the opposition's accusations that Bakiyev was not delivering on his election promises.
Kulov, a former security boss, was sprung from jail during the "Tulip Revolution" of March 2005 and teamed up with Bakiyev to help oust Askar Akayev, Kyrgyzstan's then-leader, from office.
"I have decided to ... unite and head all the fragmented but friendly political forces, all those who want radical and positive change"
former prime minister
Bakiyev and Kulov ran for election on a joint ticket after Akayev quit, becoming president and prime minister and promising to bring law and order and raise living standards.
Kulov resigned in December to ensure a new constitution went into force but was not reappointed as prime minister.
Bakiyev tried to reinstate him but gave up after parliament twice voted against his proposal, instead nominating another candidate.
Kulov said he was angry with Bakiyev for failing to help him regain his post and accused his former political ally of acting against him with "deception, dishonesty and baseness".
But a statement from the president's office said: "Felix Kulov had to leave his post of prime minister because of a disagreement with parliament, not the president."
Akayev, now in exile in Russia, said tensions were rising among various clans and ethnic groups in Kyrgyzstan.
"There is a rift between the north and the south in Kyrgyzstan, between pro-Bakiyev and anti-Bakiyev people. Inter-ethnic conflicts are on the rise," Akayev told reporters.
"There is talk about a new wave of protests this spring. I am against protests ... Our nation will not survive another revolution. It will fall apart."
Anvar Artykov, an opposition politician, said: "Of course there will be a certain level of panic in the White House," referring to the Kyrgyz government headquarters.
He said: "The authorities may resort to force to settle any crisis."
The opposition says Bakiyev has failed to carry out his election promises, and has staged several protests calling on him to resign.