Takaichi became Liberal Democratic Party (LDP) leader on October 4 but her aim to become Japan's first woman prime minister was derailed by the collapse of the ruling coalition last week.
The LDP is now in talks about forming a different alliance, boosting Takaichi's chances of becoming premier in a parliamentary vote that media reports said will likely happen on Tuesday.
Past visits by top leaders to the Yasukuni shrine in Tokyo, which honours even convicted war criminals, have angered China and South Korea, and no Japanese premier has visited since 2013.
Takaichi, seen as an arch-conservative and China hawk from the right of the LDP, has visited in the past, including as a government minister.
But on Friday, on the opening day of an autumn festival, the 64-year-old sent an offering but did not make an appearance.
Reports said she would stay away in order not to upset Japan's neighbours.
- Trump visit -
The clock is ticking for Takaichi to become Japan's fifth prime minister in as many years with US President Donald Trump due to visit Japan at the end of October.
Details of Washington and Tokyo's trade deal remain unresolved, but Trump wants Japan to stop Russian energy imports and boost defence spending.
The LDP's coalition partner of 26 years, the Komeito party, pulled the plug on their alliance on October 10.
Komeito said that the LDP has failed to tighten rules on party funding following a damaging slush fund scandal involving dodgy payments of millions of dollars.
The LDP this week began talks on forming a new coalition with the Japan Innovation Party (JIP) instead.
The two parties would be two seats short of a majority but the alliance would still likely ensure that Takaichi succeeds in becoming premier.
This is because while Takaichi needs support from a majority of MPs to become premier, in a second-round two-way runoff she only needs more than the other person.
A spanner in the works could be if opposition parties agreed on a rival candidate, but talks on this this week appeared to make little headway.
Fumitake Fujita, JIP co-head, on Thursday said the LDP and his party's policies were "very close in many areas" but said that major differences remained ahead of more talks Friday.
"If the LDP and the JIP agree to form a coalition, Takaichi will become new prime minister," Mikitaka Masuyama, a professor at the National Graduate Institute for Policy Studies, told AFP.
But he cautioned that like in recent elections, support for the LDP may continue to slide.
"It can be either way. The LDP under Takaichi may not be popular with a range of voters on the right and left that former LDP leaders Junichiro Koizumi and Shinzo Abe had enjoyed," Masuyama said.
"Or, her government may regain support from conservatives who left the LDP for other conservative opposition parties" in the July upper house election, he said.
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