LOS ANGELES — A prominent attorney, Melvyn Weiss, has agreed to plead guilty to racketeering in a lucrative kickback scheme involving payments to plaintiffs in class-action lawsuits targeting some of the largest American corporations, federal prosecutors said today.

Weiss, 72, also will acknowledge that he and others concealed secret payment arrangements that his firm, Milberg Weiss, had with named plaintiffs in the lawsuits, prosecutors said in a statement.

Under a plea deal, he could be sentenced to up to 33 months in prison and pay $10 million.

His firm dominated the industry in securities class-action lawsuits, which involve shareholders who claim they suffered losses because executives misled them about a company’s financial condition.

Authorities said the firm made an estimated $250 million over two decades by filing legal actions on behalf of professional plaintiffs who received $11.3 million in kickbacks.

Weiss’ plea deal was confirmed by an attorney, Benjamin Brafman, who represents Weiss.

Mr. Brafman did not specify the charges involved in the plea but said in a statement his client would admit “limited participation in a criminal conspiracy” involving payments to plaintiffs.

Weiss apologized in the statement.

“I deeply regret my conduct and apologize to all those who have been affected,” he said.

To conceal the scheme from judges presiding over the lawsuits and other parties in the cases, participants in the conspiracy allegedly made false and misleading statements in court documents and in under-oath depositions, prosecutors said.

“This kickback scheme lasted for more than 25 years and had a severely detrimental effect on the administration of justice across the nation as lies were routinely made to judges overseeing significant cases,” a U.S. Attorney, Thomas P. O’Brien, said. “The scheme was based in greed and it affected the integrity of the courts and the interests of an untold number of absent class members.”

Weiss previously pleaded not guilty to one count each of conspiracy, mail fraud, money laundering and obstruction of justice.

The plea deal calls for him to receive a prison sentence of 18 to 33 months, with the court able to substitute time from home confinement or community service.

Weiss also agreed to pay $10 million in fines and forfeiture penalties.

Federal prosecutors said they will ask a U.S. District Judge, John F. Walter, to impose the 33-month term after Weiss formally pleads guilty.

The kickback scheme allowed the firm’s attorneys to be among the first to file litigation and secure the lucrative position as lead plaintiffs’ counsel, according to court documents.

The lawsuits the firm filed targeted companies such as AT&T, Lucent, WorldCom, Microsoft Corp., and Prudential Insurance.

The president of the U.S. Chamber Institute for Legal Reform, Lisa A. Rickard, said the case underscores the need for federal legislation forcing more transparency and accountability of lawyers in securities litigation.

In addition, she said Congress and the Securities and Exchange Commission should undertake a review of securities class action litigation to make sure it is fair to all parties and benefits investors, not lawyers.

Weiss is expected to appear before Judge Walter within weeks to enter his guilty plea to the racketeering conspiracy count. Judge Walter is then expected to schedule a sentencing hearing.

Weiss was the fourth current or former partner of the law firm to admit criminal conduct.

With Weiss agreeing to plead guilty, there are two defendants remaining in the case — the firm itself and an attorney, Paul T. Selzer. Trials for those defendants are scheduled in August.

The first person sentenced was Seymour Lazar, a retired attorney who was ordered in January to six months in home detention and two years probation. He also was fined $600,000.

Federal prosecutors said Lazar, 80, was paid about $2.6 million to be a professional plaintiff and help the law firm, previously known as Milberg Weiss Bershad & Schulman, in its pursuit of the lawsuits.

Lazar pleaded guilty in October to obstruction of justice, subscribing to a false tax return, and making a false declaration to the court.

A former partner, William Lerach, whose high-profile legal victories included a $7 billion judgment against now-defunct energy company Enron Corp., pleaded guilty in October to one count of conspiracy to obstruct justice and make false statements.

He was sentenced last month to two years in federal prison.

Along with Lerach, other former partners who have pleaded guilty were Steven Schulman and David Bershad.

Schulman pleaded guilty to a racketeering conspiracy charge. He agreed to forfeit $1.85 million to the government and to pay a $250,000 fine.

Bershad pleaded guilty to conspiracy and agreed to cooperate with the government.

Schulman and Bershad are scheduled to be sentenced later this year.