Top government spokesman Yoshihide Suga said that Abe didn't visit the Yasukuni Shrine but donated religious ornaments marking the shrine's spring festival. The finance minister and two other Cabinet ministers prayed at the shrine.
"My understanding is that the three ministers paid visits to the shrine in their private capacity," Suga told a news conference. "There is no government comment to their shrine visits as private citizens."
Suga acknowledged reports that South Korea cancelled foreign ministerial talks but he said the talks for later this month were at planning stage and weren't official.
The shrine honors Japanese wartime leaders convicted of war crimes among 2.5 million war-dead. The shrine compound has a war museum that glorifies Japan's wartime past, and the site is a focus of nationalist pride among Japanese conservatives and right-wingers.
The visits come as Japan is at odds with South Korea over an island group in the Sea of Japan that Seoul has controlled since the 1950s and increasingly at odds as well with China over a group of small islands in the East China Sea that both countries claim.
Suga said Monday the shrine visits and donations were private and shouldn't affect diplomacy.
"Each country has its own stance on different issues. We should not let these things affect diplomatic relations," Suga added, apparently urging Seoul to calm.
Previous visits to the shrine by political leaders have been harshly criticized by South Korea, as well as China and North Korea, which bore the brunt of Japan's pre-1945 militarist march through Asia. The visits are regarded as evidence that Japan's leaders do not acknowledge their country's responsibility for its colonialist past.
Abe last visited the shrine in October, when he was opposition leader.
National Public Safety Commission chief Keiji Furuya, who paid pilgrimage to the shrine on Sunday, told reporters that he prayed as state minister but he privately paid his donation money.
"As a national lawmaker, it is only natural to offer prayers to the sacred spirits who sacrificed their lives for the country," Furuya said.