* Follows US settlement with Credit Suisse
* Leumi to record Q2 charge of 460 million shekels
(Adds details, share reaction, background, source comments)
JERUSALEM, June 8 (Reuters) - Bank Leumi, Israel's second largest bank, said on Sunday it was close to a deal to pay nearly 1 billion shekels ($289 million) to the U.S. Justice Department in relation to its investigation into possible tax evasion by the bank's American clients.
The settlement, likely to take weeks or months to complete, marks another step in the United States' wide-ranging efforts to crack down on Americans using offshore banks to evade taxes. Last month, Credit Suisse agreed to pay more than $2.5 billion in penalties for helping Americans dodge taxes.
Leumi, which had already set aside 490 million shekels, said it would increase this by 460 million to make a total of 950 million. The bank will record this charge in the second quarter which would significantly impact quarterly results, it said.
"In order to settle all the issues related to the U.S. customers matter, the bank continues to hold discussions with additional relevant U.S authorities," it said.
Leumi said the investigation covered the period between 2002 and 2010. "Leumi is the first bank in the Israeli banking system expected to reach an agreement with the U.S. Justice Department," the bank said.
A source familiar with the negotiations said Leumi was notified of the offer by U.S. authorities last week. The United States did not want the offer size published but Leumi had no choice but to inform its shareholders under Israeli law.
Leumi has urged U.S. clients to disclose information about their accounts to the U.S. authorities.
The U.S. effort has been focused largely on banks in Switzerland, but banks in other countries, including Israeli banks through their Swiss units, are under scrutiny.
In January, the Justice Department said it had received 106 requests from Swiss entities to participate in a U.S. settlement programme aimed at ending the tax-dodging probe.
Hapoalim, Israel's largest bank, as well as Mizrahi-Tefahot - Israel's fourth-largest bank - are also being investigated.
Spokespeople for Hapoalim and Mizrahi declined to comment on the progress of the investigation at the banks.
The probe at Israeli banks started in 2011, two years after Swiss bank UBS was fined $780 million and also had to hand over client data to the United States.
The source, who declined to be identified, estimated Israeli banks' exposure to the U.S. tax issue at 4-5 billion shekels.
The source said Leumi did not initially realise it had done anything illegal. "Clearly, Leumi didn't respond quickly enough," the source said. "Leumi didn't fully understand the meaning of the investigation."
Leumi decided to cooperate fully with the United States, believing that this could result in a lower settlement. It conducted its own investigation.
Leumi's shares closed 0.5 percent lower in Tel Aviv, compared with gains of 1 percent on the broader bourse.
($1 = 3.4574 Israeli Shekels)
(Additional reporting by Ari Rabinovitch in Jerusalem and Katharina Bart in Zurich. Editing by Jane Merriman)