Mr Lerner, detained as he tried to leave Israel, is alleged to have defrauded Russian banks of $85m (pounds 52m), and to have been involved in two murders.
Natan Sharansky, once the most famous Jewish dissident in the Soviet Union and now Israel's Trade and Industry Minister, admits receiving $100,000 from Mr Lerner, who changed his name in Israel to Zvi Ben-Ari. The politician says he gave the money to an organisation which helps Russian Jews emigrate to Israel.
Mr Lerner had meetings with other ministers and political leaders, but it is not known how many of these received financial aid.
The arrest of Mr Lerner is the first time the police have arrested a Russian Jewish emigrant suspected of leading a crime syndicate.
Israel is used by the Russian mafia for laundering money and for holding meetings, which is easy to do without attracting attention because at least 800,000 Israelis are Russian-born. Israeli currency laws are lax, to allow immigrants to bring money into the country safely.
The Israeli police said earlier this year that they knew of 31 Russian mafia leaders in Israel, of whom only one is Jewish; the rest forged documents or arranged marriages to become Israeli citizens. Mr Lerner came to Israel in 1990. At this time, the Russian mafia held many of its meetings in Cyprus, but in 1993 switched to Tel Aviv to avoid the attention of foreign police forces.
The Lerner affair is exacerbating a row between Mr Sharansky and his former close friend, Benjamin Netanyahu, the Prime Minister. Accusing Mr Netanyahu of failing to keep his promise to allow Mr Sharansky's party, Yisrael Ba'Aliya, to choose the Israeli ambassador to Russia, Mr Sharansky last week refused to attend the weekly cabinet meet- ing. Aides to Mr Netanyahu said Mr Sharansky was simply hoping to divert attention from his party's links to Mr Lerner.
The Russian mafia, also known as the Organizatsiya, grew up in the Soviet Union in the Seventies and Eighties.
Many gangsters moved to New York in the first wave of Jewish emigration, though only one-third were really Jewish, police say.
The mafia had about 300 members, prepared to use extreme violence to gain control of the drugs trade and other rackets.