The paralysis born of a divided parliament has prevented the appointment of a new Bank of Japan governor and sparked speculation that Fukuda's ruling party might try to replace him ahead of a general election that could come this year.
No election for the powerful lower house need be held until September 2009, and Fukuda is reluctant to call a poll that would likely see the ruling camp lose its huge majority.
But the main opposition Democratic Party is pressing for an early poll and some pundits say Fukuda -- or his successor -- might be forced to call one to seek a mandate for dealing with the deadlock.
"There is only a short time left, but I have not given up," the 71-year-old Fukuda told a hastily called news conference, referring to the gasoline tax.
"I believe we can achieve a breakthrough if the ruling and opposition parties talk," Fukuda said, adding he wanted to hold talks with main opposition Democratic Party leader Ichiro Ozawa.
The Democrats, which with smaller allies control parliament's upper house and can delay laws as well as veto appointments, wants to abolish a "provisional" gasoline tax whose revenues are devoted to road construction.
Democrats and other critics say the three-decade-old tax is a symbol of the long-ruling Liberal Democratic Party's (LDP) practice of wasteful spending on vested interests.
The Democrats also want to free up other revenues dedicated to road construction and maintenance for general spending.
In a concession to that demand, Fukuda proposed reallocating tax revenues now earmarked for building roads to general spending from fiscal 2009/10.
But he refused to budge on the government's proposal to extend the temporary gasoline tariff in the fiscal year from April 1, saying abolishing the tax now would leave a huge revenue gap in national and local budgets.
"The proposal to shift road revenues to general spending from fiscal year 2009/10 is a step forward, but as for the provisional tax rate, it is close to an empty response," Democratic Party Secretary General Yukio Hatoyama told reporters.
