The state attorneys-general, which is suing the US treasury department, says that the federal government did not attempt to locate those who had not cashed in their bonds at the time of maturity.
"It's better for the millions of American who are the rightful owners to have it returned to the states, because the states will make a real effort to find them," David Bishop, a partner at Kirby McInerney who is representing the states in the suit, said.
"And if after searching for them they can't find them, the money can go to work in the communities where the bonds were purchased."
The states would be obligated to pay bond holders no matter if it take decades for the bonds to be located.
But states could use the interest earned on such unclaimed money for schools or other purposes.
The treasury department has said that it tries to locate holders of unclaimed bonds, and that people can type their social security number into its web site to see if they have a bond.
"One of the misunderstandings [about bonds] out there is that there is a lot of cash sitting somewhere in a drawer. Money from savings bonds was used to run the daily operating expenses of the government," Joyce Harris, from the Bureau of the Public Debt, said.
"These are obligations of the federal government, not the states. There is no pot of gold out there just waiting for someone to grab it."
The treasury also points out that most of the unclaimed bonds are more recent than the original World War II-era certificates.
Harris said that many holders of the bonds often choose not to cash them in on maturity due to tax reasons or even a sense of patriotism from the war.
"Quite frankly, people are aware of the bonds," she said. "A majority, when you contact them, are aware of the bonds."
The complaint was first filed in Federal court in New Jersey in 2004 with New Jersey and North Carolina as the plaintiffs.
Montana, Kentucky, Oklahoma and Missouri later joined the case.