The attempt by all 16 members of the government to resign followed a critical vote in parliament last week.
The resignations also came amid mounting street protests and fears of politically inspired violence in the impoverished but strategically placed ex-Soviet republic, which hosts both Russian and US military bases.
“The entire government resigned, but the president did not accept,” Deputy Prime Minister Adakhan Madumarov said. “We consider we have not got the moral right to stay in our posts after the parliament’s unsatisfactory evaluation of our work.”
However, because of Mr Bakiyev’s refusal to accept the resignations, “we are still working. We are obliged to … under the constitution,” he said.
Kyrgyzstan, sandwiched between China, Kazakhstan, Tajikistan and Uzbekistan, has come under growing international scrutiny since a revolution in March 2005 overthrew veteran leader Askar Akayev.
A popular movement led by Mr Bakiyev and the current prime minister, Felix Kulov, drove out Mr Akayev in street protests against disputed elections and corruption among the elite.
However, Mr Bakiyev and Mr Kulov have since come under fire for not carrying out promised reforms quickly enough or reducing the chaos that has seen three members of parliament assassinated in the last year.
The attempted mass resignation and Mr Bakiyev’s refusal to accept it “shows the country is on the edge of a serious political crisis,” independent political analyst Nur Omarov said.
The latest blows for the former revolutionary leaders saw parliament on Friday slam the government’s poor performance, followed Saturday by a 10,000-strong rally demanding action against corruption and crime within a month.
The European Union said that it was alarmed at the level of political violence and the rise in organised crime.
“We note with concern a number of … cases of political violence in Kyrgyzstan, including the murders of three members of the Kyrgyz parliament,” the EU said in a statement.
“We are concerned that this violence leads to a climate of insecurity and intimidation that could undermine the efforts undertaken by Kyrgyzstan to build a stable, inclusive and prospering democracy.”
The 25-nation bloc said it was also alarmed by reports that suspected mafia boss, who faces murder charges, had just been elected to the national assembly of the central Asian state.
“There are worrying indications that circles connected with organised crime are attempting to gain influence over political life and state institutions in Kyrgyzstan,” it said.