One of the For Reform movement's leaders, Edil Baisalov, told RFE/RL's Kyrgyz Service today that Kulov and his government have no widespread support among lawmakers.
Baisalov said that, in his view and that of other For Reforms leaders, Kulov's voluntary departure would help avert the risk of new political crises.
"In our opinion, a very simple and decisive step would be for Feliks Kulov to resign," Baisalov said. "We would then be in a position to set up a new government in accordance with the new constitution and that government would be able to work within the legal framework of this new constitution."
Baisalov heads a nongovernmental organization known as the Coalition For Democracy and Civil Society.
He was one of the organizers of the nearly weeklong demonstration that began in the capital on November 2 and eventually forced President Kurmanbek Bakiev to agree on a revamped constitution that reduces the powers of the presidency to the benefit of the legislature.
Kulov has said he has questions about the new basic law and rejected calls for his resignation.
Former Foreign Minister Roza Otunbaeva -- another For Reforms leader -- today warned Kulov that he should abide by the new constitution and work "for the benefit of every Kyrgyz citizen."
Otherwise, Otunbaeva said, his government may "not live long."
Demonstrators in early November had demanded that Bakiev, Kulov, and his team usher in the constitutional reforms or step down.
The country's previous president, Askar Akaev, was forced to flee to Russia in March 2005 in the face of public demonstrations and the storming of government facilities by opponents who at the time were allied with Bakiev and Kulov.
More little more than a year later, opposition politicians had accused the new government of balking at promised reforms.