Support for Prime Minister Shinzo Abe has so far withstood graft allegations against the chief engineer of his Abenomics policies. His ability to ride out the storm before summer elections may hinge on how convincing an explanation Economy Minister Akira Amari offers this week.

Amari is set to hold a news conference Thursday on allegations in the Shukan Bunshun magazine last week that he and his secretaries accepted at least ¥12 million in undeclared donations from a construction company. Amari initially said he could not recall details and pledged a public explanation after reviewing the facts.

The accusations have prompted speculation Amari may face pressure to resign, and opposition Democratic Party of Japan leader Katsuya Okada told the Diet on Tuesday that Abe also had a "serious" responsibility to provide an explanation.