Ministry wants higher budget allocation; P.M. vows to get tough in island dispute.
May help determine Prime Minister Shinzo Abe's decision on how to proceed with a planned increase in sales tax.
Visits to the shrine by gov't officials routinely anger Japan's neighbors.
P.M. Abe unlikely to visit shrine, though he did send two cabinet members there, potentially inflaming regional tension.
Seen as symbol of World War II-era militarism and likely to inflame China relations.
Abe seeks to show he has a strategy to both foster an economic recovery and contain the country's enormous public debt.
The world's third-largest economy grew by an annualised 2.6% in April-June, but below both market expectations and Q1.
Abe government has flagged second-quarter GDP number as key test.
Opponents of tax increase within government said to be gaining traction.
Hawkish P.M. cites nation's unique duty to wipe out nuclear weapons worldwide.