The government may need to issue bonds to meet the costs but should not do so without coming up with ways to pay for redemption, Yosano said, signaling that some form of tax hike would be inevitable.
"If we were to issue bonds for reconstruction, we need to decide in how many years we would pay the money back and how. That's important in maintaining market trust in Japan's fiscal state," he said.
Japan is reeling from the triple disaster of an earthquake, tsunami and prolonged nuclear crisis, with the government struggling to find ways to pay for the biggest reconstruction effort since the aftermath of World War Two.
Damage from the quake pushed Japan into recession with the economy shrinking much more than expected in the first quarter and set to contract again in April-June as power shortages and supply chain disruptions hit factory output.
The government earlier this month passed through parliament a 4-trillion-yen first extra budget to meet immediate disaster relief costs.
It plans to compile a sizable second extra budget for reconstruction, although lawmakers are divided on how to pay for the spending.
Japan's public debt, at double the size of its $5 trillion economy, is the biggest among major industrialized economies, limiting room for additional fiscal stimulus.
But lawmakers are hesitant of raising tax, particularly the politically sensitive sales tax, for fear of scaring voters away, even as the cost of quake reconstruction adds to the huge social welfare spending for a rapidly aging society.
Yosano, regarded as a fiscal hawk, has said that raising tax is crucial for Japan to meet ballooning social welfare costs and fix the country's tattered finances. ($1 = 81.610 Japanese Yen)