Wealthy U.S. individuals with hidden offshore bank accounts will get an extra three weeks to participate in an amnesty program that could help them avoid criminal prosecution, U.S. tax officials said on Monday.

The Internal Revenue Service extended the program to October 15, citing pleas from tax professionals who say they could not handle the numbers rushing to take part.

The IRS began the offer in March, soon after giant Swiss bank UBS AG turned over the names of some account holders as part of a $780 million criminal settlement with the U.S. government. It is part of a broader crackdown on tax evaders as countries hunt for revenue in the global recession.

IRS officials and lawyers have been saying for months that the response to the voluntary disclosure program has been unprecedented. More than 3,000 taxpayers have come forward, compared with fewer than 100 for all of last year.

By extending the deadline for a short period of time, the IRS is providing relief for those who had intended to come forward prior to the deadline, but face logistical and administrative challenges in meeting it, the agency said.

The IRS said there would be no further extensions. The prior deadline was September 23.

In exchange for coming clean by the deadline, individuals would pay back taxes and a reduced fine, while generally avoiding criminal prosecution.

After months of tortuous negotiations that involved the Swiss government and challenged that country's tradition of banking secrecy, UBS agreed in August to disclose the names of 4,450 American holders of secret accounts at the bank, ending a civil lawsuit.

The first batch of UBS account holders began to get letters from the bank last week, warning them that their names could be turned over to U.S. tax authorities.

There is a hazard that when you do this, you are bending to the interests of people who are trying to find out if their names will be disclosed, said Washington-based lawyer George Clarke of Miller Chevalier, who said his clients were pleased.

The UBS warning letter said that both direct numbered accounts and accounts set up though offshore entities would be targeted by the IRS as part of the UBS settlement.

That surprised some, as the first group would include people who inherited accounts long ago, including some whose relatives perished in the Holocaust.

Although the IRS said tax professionals had been overwhelmed, many believe the agency itself could use more time to process the applications and might also be making a bet that it could reel in bigger fish.

Those with more sophisticated means will continue to conceal their assets, and in theory, be the last holdouts, said William Sharp, an attorney with Sharp Kemm in Tampa who is counseling clients taking part in the amnesty program.

After the August civil settlement between UBS and the U.S. government, for example, clients with bigger portfolios starting walking in his door, Sharp said.

(Additional reporting by Pascal Fletcher in Miami and Jonathan Stempel in New York; Editing by Lisa Von Ahn and Gerald E. McCormick)