WASHINGTON — The federal government announced on Tuesday that it intends to pay $3.4 billion to settle claims that it has mismanaged the revenue in American Indian trust funds, potentially ending one of the largest and most complicated class-action lawsuits ever brought against the United States.

The tentative agreement, reached late Monday, would resolve a 13-year-old lawsuit over hundreds of thousands of land trust accounts that date to the 19th century. Specialists in federal tribal law described the lawsuit as one of the most important in the history of legal disputes involving the government’s treatment of American Indians.

President Obama hailed the agreement as an “important step towards a sincere reconciliation” between the federal government and American Indians, many of whom, he said, considered the protracted lawsuit a “stain” on the nation.

As a presidential candidate, Mr. Obama said, “I pledged my commitment to resolving this issue, and I am proud that my administration has taken this step today.”

For the agreement to become final, Congress must enact legislation and the federal courts must then sign off on it. Administration officials said they hoped those two steps would be completed in the next few months.

The dispute arises from a system dating to 1887, when Congress divided many tribal lands into parcels — most from 40 to 160 acres — and assigned them to individual Indians while selling off remaining lands.

The Interior Department now manages about 56 million acres of Indian trust land scattered across the country, with the heaviest concentration in Western states. The government handles leases on the land for mining, livestock grazing, timber harvesting and drilling for oil and gas. It then distributes the revenue raised by those leases to the American Indians. In the 2009 fiscal year, it collected about $298 million for more than 384,000 individual Indian accounts.

The lawsuit accuses the federal government of mismanaging that money. As a result, the value of the trusts has been unclear, and the Indians contend that they are owed far more than what they have been paid.

Under the settlement, the government would pay $1.4 billion to compensate the Indians for their claims of historical accounting irregularities and any accusation that federal officials mismanaged the administration of the land itself over the years.

Each member of the class would receive a check for $1,000, and the rest of the money would be distributed according to the land owned. In addition, legal fees, to be determined by a judge, would be paid from that fund.

Philip Frickey, a law professor at the University of California, Berkeley, who specializes in federal Indian law, said that of all the Indian land claims and other lawsuits over the past generation, the trust case had been a “blockbuster” because it is national in scope, involves a large amount of money, and has been long-running.

The lawsuit spanned three presidencies and engendered seven trials covering 192 trial days, generated 22 published judicial opinions, and went before a federal appeals court 10 times.

Over its course, the federal judge originally assigned to the case, Royce C. Lamberth, put contempt orders on two secretaries of the interior over their handling of the lawsuit. In 2006, after the Bush administration complained of bias, a federal appeals court removed Judge Lamberth from the case.

Judge James Robertson has handled it since, and he pushed both parties to negotiate — including brokering a last-minute deal over an undisclosed problem that nearly derailed the settlement late Monday, said David J. Hayes, the Interior Department deputy secretary.

Attorney General Eric H. Holder Jr. on Tuesday characterized the case as “intense, and sometimes difficult.”

“The United States could have continued to litigate this case, at great expense to the taxpayers,” Mr. Holder said. “It could have let all of these claims linger, and could even have let the problem of fractionated land continue to grow with each generation. But with this settlement, we are erasing these past liabilities and getting on track to eliminate them going forward.”

The settlement also seeks to resolve an ever-growing headache of the trust system that contributed to the government’s problems — especially in the pre-computer era — in keeping track of the allotments: the original owners, most of whom died without leaving wills, have many heirs, which has “fractionalized” the ownership interests.

For example, one 40-acre parcel today has 439 owners, most of whom receive less than $1 a year in income from it, Mr. Haynes said. The parcel is valued at about $20,000, but it costs the government more than $40,000 a year to administer those trusts.

In an effort to resolve such problems — and prevent them from worsening in subsequent generations — the settlement would establish a $2 billion fund to buy fractional interests in land from anyone willing to sell. The program would seek to consolidate ownership in parcels of land for the tribes, while reducing the Interior Department’s work in keeping track of the trusts.

“This is an historic, positive development for Indian country,” said Ken Salazar, the Interior Department secretary, “and a major step on the road to reconciliation following years of acrimonious litigation between trust beneficiaries and the United States.”

Over the years, the plaintiffs have contended that they were owed tens of billions of dollars, while the government has at times taken the position that it owed them little or nothing.

Elouise Cobell, the lead plaintiff who filed the class-action lawsuit in 1996, said she believed that the Indians were owed more, but that it was better to reach an agreement that could help impoverished trust holders than to spend more years in court. She said she had originally expected the litigation to last only two or three years.

“We are compelled to settle by the sobering realization that our class grows smaller each day as our elders die and are forever prevented from receiving just compensation,“ Ms. Cobell said.

Robert Clinton, an Arizona State University law professor who specializes in federal Indian law, said the settlement alone would not resolve the trust problem because many of the heirs who own tiny interests in parcels may not be willing to sell them.

Still, the settlement will provide an incentive for such owners to sell: the Interior Department will set aside up to 5 percent of the value of the land interests for a scholarship fund to help Indians attend college or vocational school.