The front-runner in the race to succeed Japan's Prime Minister Junichiro Koizumi made a secret visit to a controversial war shrine, reports say.
Mr Abe refused to confirm or deny he had visited
Chief Cabinet Secretary Shinzo Abe did not confirm or deny he had visited, but said the war dead deserved respect.
The alleged visit was criticised by Finance Minister Sadakazu Tanigaki, seen as the main rival to replace Mr Koizumi, who steps down in September.
Neighbouring countries strongly oppose visits to the Yasukuni Shrine.
They say the shrine honours Japan's militarist past, because 14 Class A war criminals are among the 2.5 million war dead commemorated there.
The issue has led to a sharp downturn in diplomatic ties with China and South Korea, with Beijing suspending top-level summits with Tokyo.
Mr Koizumi's potential successors have come under pressure set out whether or not they would visit the shrine.
Mr Abe has visited Yasukuni on several occasions in the past, but the April visit, if true, would have been his first since he was appointed Cabinet Secretary.
On Friday, he said his desire to pay his respects to the war dead had not changed, but refused to be drawn on his future plans
"Since this had developed into a diplomatic and political issue, I have said that I have no intention to say whether I would or would not go there or have or have not visited there, and this stance has not changed," he said.
Built in 1869 to honour victims of the Boshin Civil War
Now venerates the souls of 2.5m of Japan's war dead
Those enshrined include 14 Class A war criminals
Two polls last month suggested that more than half of the Japanese public do not want their next prime minister to continue the visits.
There is also pressure from the business community, who fear that the ongoing row could harm economic ties.
Mr Tanigaki has said that he will not visit the shrine and spoke out against Mr Abe's reported visit.
"A person who holds the position in the Prime Minister's Office needs to consider diplomatic issues," he said.
Another potential candidate, Foreign Minister Taro Aso, is also thought to be inclined against the visits.
Mr Abe's unconfirmed April visit drew immediate reaction from South Korea. "It's regrettable if that is true," Foreign Ministry spokesman Choo Kyu-ho said.