Fukuda said: "In that sense, I believe the government bears responsibility in various ways, including moral responsibility.
"I expect we'll be discussing the matter further in the [ruling] party as we work on this."
He also said he intended to meet the group seeking damages and referred to proposed legislation aimed at providing aid to about 1,000 hepatitis C sufferers.
Japanese media say about 800 more people are expected to file suits.
The plaintiffs say they contracted hepatitis C while using defective blood-clotting medicines, mostly in the 1980s, and claim the government and the drug-makers continued to use the medicines, despite knowing they were potentially contaminated.
The drug-makers are Nihon Pharmaceutical, Mitsubishi Pharma (now called Mitsubishi Tanabe Pharma) and its subsidiary Benesis.
Four of the five courts have ordered the defendants to compensate dozens of patients and the Osaka High Court issued a settlement proposal in November.
The two sides have since attempted to reach an out-of-court settlement, although negotiations have become bogged down over how the plaintiffs would be compensated.
On Sunday, Fukuda said his ruling bloc would submit legislation, drafted in consultation with the main opposition Democratic party, to provide aid to tainted patients.
Although as many as 10,000 people may have been infected through the products, only the 1,000 lawsuit participants are expected to be eligible for the aid.
The drug-makers have said little on the issue, other than that they were keeping a close eye on the progress of the lawsuits.
Hepatitis C is a chronic, blood-borne virus that can cause damage to the liver leading to cancer, cirrhosis and liver failure. It is treatable, but many people who have the disease do not know they are infected.