Bakiyev had set a June 1 deadline for an agreement on base payments, warning that U.S. forces would no longer be welcome in the Central Asian state if no deal was reached by then.
But on Thursday, Kyrgyz and U.S. officials were "actively moving ahead" in talks on the matter in the capital Bishkek, according to a statement from the Bakiyev's office.
A decision has been reached to continue the talks "beyond June 1 and complete them in the nearest future," the statement said.
Both sides are keen "to come to a mutually beneficial agreement" based "on the positive development of Kyrgyz-American relations and the recent deterioration of the situation in Afghanistan and the increased activity of terror groups in Central Asia," Bakiyev's office said in a statement.
The impoverished Central Asian nation had proposed that the U.S. pay US$200 million (Ђ155 million) a year - a 10-fold increase - for use of the base, which has supported U.S.-led operations in nearby Afghanistan since 2001.
U.S. officials have said they are ready to pay more for use of the base, but have declined to give figures, the AP reports.
The base took on greater importance after neighboring Uzbekistan expelled U.S. forces from a base there last year.
Kyrgyzstan also hosts a Russian base near Bishkek, and appears to be under pressure from Russia and China to expel U.S. forces.
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