The United Front led by Felix Kulov, a former presidential ally in the 2005 coup, Thursday issued an ultimatum to Bakiyev to sign a draft constitutional law delegating part of his powers to parliament by April 6.
The opposition said it would seek the president's immediate resignation unless he agreed to share his powers with parliament within 24 hours.
In response to the ultimatum, the Kyrgyz president conceded that the current Constitution had many flaws but he said it cannot be constantly changed under pressure of a political crisis.
"We have changed our main law twice recently and both times it was done in the middle of a political struggle," Bakiyev said in an interview with RIA Novosti.
"We cannot afford to do this over and over again, making the Constitution a sacrificial lamb," he said, adding that a special working group on constitutional changes that included many opposition members had been created.
"I hope that experts will be able to prepare a well-considered and mutually-acceptable draft document and introduce it in parliament in the next few days," Bakiyev said.
He said the new draft of the Constitution should meet the interests of all political forces in the country and strengthen all three branches of power.
"I will seek political dialogue with any political forces," Bakiyev said. "And when I feel that they are right I will be willing to make changes."
"I do not think it is a weakness," the president said. "On the contrary, I see a real political acumen in this attitude - being able to accept opposing opinions, to recognize mistakes, to change the situation."
Opposition protests last fall resulted in the adoption of a new constitution that delegated much of the president's authority to the legislature, effectively turning Kyrgyzstan into a parliamentary republic. In December, however, parliament voted in another constitution draft, which returned to the president virtually all previously ceded powers.
The new draft constitutional law, the third proposed by the opposition in the impoverished Central Asian republic in the past few months, stipulates that the prime minister shall be appointed by parliament, and ministerial candidates coordinated with the president.
Bakiyev appointed a liberal opposition leader, Almaz Atambayev, new premier in late March, and instructed him to form a coalition government. But opposition members refused to join the new government, saying it would change nothing, so some posts are still vacant in the Cabinet.
Felix Kulov previously said "power will be peacefully transferred on April 11", the date for mass protests promised by the opposition.
Bakyev said Friday that the authorities were not worried about possible public disturbances during the scheduled opposition rallies, although law enforcement agencies were ready to prevent any violence.
"I will take most stringent measures to prevent any violations of law and order and to punish those who would attempt such actions," the president said. "And the country knows about it."
