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Mr Amari unexpectedly made the announcement at a press conference in Tokyo on Thursday.
But he again denied personally receiving bribes from a construction company, as had been alleged by a Japanese magazine.
The development will be seen as a significant blow for Prime Minister Shinzo Abe.
Mr Amari, who has been minister of state for economic and fiscal policy since late 2012, has been widely described as one of Mr Abe's most trusted members of parliament.
As Japan's lead negotiator for the Trans Pacific Partnership (TPP) agreement, Mr Amari was expected to travel to New Zealand next week to sign the agreement.
A local magazine had reported last week that Mr Amari and his aides were given money and gifts worth some 12m yen ($101,000; £70,500) by a construction company in return for some favours linked to land ownership.
Mr Amari said he did receive money which he wanted declared as a political donation, however, he said some of it was mishandled by his staff.