Japanese Prime Minister Shinzo Abe apologised again on Sunday over his suspected cronyism scandal and cover-up caused anxiety and loss of confidence in his government.

Abe faces his biggest political crisis since taking office in December 2012 as suspicions swirl about a sale of state-owned land at a huge discount to a nationalist school operator with ties to his wife.

Abe, at his ruling party's annual convention, said he as head of the government feels his responsibility for the scandal, but offered no sign of stepping down while his ratings in a slump.

The Liberal Democratic Party (LDP) at the convention also adopted a proposal to revise Japan's pacifist constitution in line with a plan floated by Abe last year to explicitly refer to the Self-Defense Forces (SDF), as Japan's military is known.

Hundreds of protesters, near the National Diet building, urged Abe to resign, claiming that revising the constitution's war-renouncing Article 9 will open the way to a bigger role for the military overseas.

Public opinion polls last weekend showed support for Abe's cabinet sinking as low as 31%, with majorities saying he bears some responsibility for the affair.