Addressing about 4,000 protesters gathered outside the government's headquarters, one of Bakiyev's aides said that the decision was taken in order to avoid bloodshed.
Bakiyev, the aide told the crowds, had signed a decree sacking Osmonali Guronov and appointing Omurbek Suvanaliyev as the new interior minister.
Suvanaliyev then climbed onto the protesters' own loudspeaker truck to address them.
"I want to assure you on behalf of the Kyrgyz police that the police will not fire on its own people," he said.
"We are with the people. Let's keep order here and find a political solution to political demands. There will be no use of violence against you while I am minister."
Opposition demand change
The new minister is widely respected by the opposition and his first act was to sack the unpopular head of Bishkek's police force.
"He is a democratic general," said Edil Baisalov of the Opposition For Reform movement.
But opposition leaders dismissed the appointment of the new minister as a tactical move by Bakiyev to buy time.
Anti-government protests have centred on Bishkek, the capital
"We will not leave here until Bakiyev quits," Temir Sariyev, another opposition leader, said.
Bakiyev's 16-month rule has been marked by a standoff with his opponents in parliament who are demanding he make constitutional changes to reduce his powers.
He submitted his proposed changes to parliament on Monday, but his failure to appear in parliament inflamed sentiment.
Protests outside parliament, which had been growing smaller, gained new momentum and moved to the White House, the president's official residence.
Al Jazeera's reporter at the scene reported that some of the presidental guards had deserted their positions and joined the protesters.Güncelleme Tarihi: 20 Eylül 2018, 18:16