(Adds comments on government, details on digital bank)
By Ari Rabinovitch
TEL AVIV, April 1 (Reuters) - Israel's Bank Leumi is in talks with the U.S. Securities and Exchange Commission (SEC) and could be required to make payments to the watchdog over securities held by its U.S. clients, it said on Wednesday.
Leumi, Israel's second-largest lender, has already agreed to pay $400 million to the Department of Justice and New York state to settle two separate investigations into whether the bank helped its U.S. clients to evade taxes.
Though the bank's chairman David Brodet told a press briefing on Wednesday that the December settlement had lifted "a heavy cloud of uncertainty", Chief Executive Rakefet Russak Aminoach said that an issue remains over whether any laws were broken regarding securities held by Leumi's U.S. clients.
Aminoach said the bank is talking to the SEC but it is unclear whether there will be any further repercussions.
"We have no idea whether there is a matter we will have to pay for," she said.
"I can say only that if you look at all agreements made around the world in an issue similar to ours, if in the end someone paid the SEC, it was always minor and negligible compared with the size of the agreement.
"We assume that also for us, if there is (a payment), it will not be significant."
STABILITY
Brodet, a former director general of Israel's Finance Ministry, also called on the country's new government and the reformist politician who is front-runner for becoming finance minister, not to shake stability in the banking sector.
Prime Minister Benjamin Netanyahu has offered the powerful finance minister post to Moshe Kahlon, who during his campaign for the March 17 parliamentary election spoke of opening the sector to new competition by adding Internet banks and similar initiatives.
Leumi and Hapoalim, Israel's biggest bank, have a combined market share of about 60 percent.
"We are not worried about increasing competition because we are used to it," Brodet said at the press briefing. "I expect for there to be a dialogue, real and matter-of-fact between us ... And let's remember that things have to be done in a way that doesn't hurt the stability of the banks."
Leumi said on Wednesday it planned to launch a digital bank in 2016, one that does not have individual branches and is completely accessible to clients over their mobile devices.
(Editing by David Goodman and Susan Thomas)