Tokyo (AFP) - Three nationalist ministers in Japan's cabinet paid homage at a war shrine hated by China Saturday, despite tentative signs of a thaw in Tokyo's long-frozen relationship with Beijing.

The visits to Yasukuni by three of the five women in Prime Minister Shinzo Abe's cabinet came as a fourth -- the moderate daughter of a former premier -- reportedly mulled resignation over a cash scandal.

They also come after what appeared to be a breakthrough in Sino-Japanese ties, with a handshake between Abe and Chinese Prime Minister Li Keqiang on the sidelines of an international gathering in Italy.

Abe has set his sights on a summit with Chinese President Xi Jinping -- his first -- when Beijing hosts a meeting of the Asia Pacific Economic Cooperation bloc (APEC) next month, and had been talking up the head-to-head in the hope of bouncing China into the meeting.

But a mass visit to Yasukuni on Friday by 110 lawmakers provoked a rebuke from Beijing.

Then in what has become a standard way for China to signal its annoyance with Japan, official Chinese ships were Saturday sent into waters around islands at the centre of a long-running territorial dispute between the two.

The pilgrimage to Yasukuni by three of Abe's ministers -- all well-known for their strident nationalist views -- will likely do little to curry favour abroad, including in key ally the United States, but will play well with a core group of right wing supporters at home.

Internal Affairs and Communications Minister Sanae Takaichi, who was first to the shrine on Saturday morning, made international headlines last month when a picture emerged of her standing alongside the leader of a domestic neo-Nazi party.

National Public Safety Commission chief Eriko Yamatani, who has also been pictured with fringe right-wingers, and Haruko Arimura, the state minister in charge of female empowerment, also paid homage.

The 145-year-old Shinto shrine is the supposed repository of the souls of some 2.5 million citizens and soldiers who died in World War II and other conflicts.

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It is controversial because they include senior figures in the WWII administration, such as General Hideki Tojo, who ordered the attack on Pearl Harbor.

It is seen as a symbol of Japan's militarist past, and the continued observance of festivals there by public officials is taken as proof in neighbouring countries of Japan's lack of repentance for its warring.

- 'Gravely concerned' -

China lashed out Friday after the mass lawmakers' visit, saying it was "gravely concerned" by the activity.

"China would like to reiterate that Sino-Japan relations can only realise healthy and stable development when Japan seriously faces up to and repents of its aggressive past and disassociates itself with militarism," a statement said.

While China gets publicly annoyed by politicians' visits to the shrine, it would likely react very strongly to the prime minister going to Yasukuni.

Since a trip in December 2013, Abe has stayed away, although he made offerings for the spring festival, on the war anniversary on August 15 and again on Friday.

He is thought unlikely to visit the shrine after he returns home Saturday from Italy.

Instead, he is likely to turn his attention to damage limitation in the wake of the cash-scandal that has erupted around one of his most popular ministers.

The loss of Yuko Obuchi, a telegenic mother-of-two who is in charge of Japan's energy sector, would be a blow to his bid to convince Fukushima-scarred voters the country's shuttered nuclear reactors are safe to turn back on.

Obuchi has told sources close to Abe that she intends to resign when the prime minister gets home, the Nikkei business daily reported.

That follows reports that her political funds have been misspent, including on make-up, theatre tickets for supporters and accessories.

However, after a feverish morning of speculation and rumour in Tokyo's political world, Obuchi appeared to be rowing away from an immediate resignation.

"What I must do now is thoroughly investigate my own political fund," she told reporters.

"I have no plans" to meet Abe, she said.