TOKYO, Sept 13 (Reuters) - Japan's ruling party scrambled on Thursday to find a new leader and avoid a policy vacuum after Prime Minister Shinzo Abe's shock resignation the previous day.

Abe had said he was quitting over the stalemate in parliament but senior officials said health problems were also a factor, and public broadcaster NHK reported that the prime minister had been admitted to hospital after medical checks.

Abe's year in office has been marked by scandals involving cabinet members and a disastrous election defeat in July.

But the conservative leader's decision to step down now sparked a barrage of criticism and concern that the ensuing confusion could stall vital decisions on policies such as tax and fiscal reform.

Liberal Democratic Party (LDP) Secretary-General Taro Aso, a close Abe ally, is seen by many as frontrunner to take over, but any successor will still face a deadlock in parliament.

The main opposition Democratic Party, which with small allies won control of the upper house in the July election and can delay legislation, is against extending a Japanese naval mission in support of U.S. military operations in Afghanistan.

Other diplomatic efforts could also be affected. Abe, an advocate of a bolder foreign policy who thawed chilly ties with Beijing, had been expected to visit China this year to keep up that momentum.

"It is questionable whether just replacing the prime minister will break through the political confusion," the Nikkei business daily said in an editorial. "No matter who is the next prime minister, managing the administration will be extremely tough."

Abe's aides have not commented on speculation that a soon-to-be-published tabloid magazine article on suspicions he had evaded taxes had prompted his departure.

Japanese stocks edged up, recovering ground lost after Abe's abrupt announcement, while the yen was steady in a market focused on a weak dollar and other global market issues.

RACE FOR THE TOP

Aso may be frontrunner to succeed Abe, who will stay as caretaker until he is replaced, but his closeness to the prime minister and a record of gaffes leaves doubts as to whether his victory is assured, analysts said.

Finance Minister Fukushiro Nukaga said he had decided to run, while other names floated include former finance minister Sadakazu Tanigaki, former chief cabinet secretary Yasuo Fukuda, and party heavyweight Taku Yamasaki.

Some lawmakers petitioned for the return of Abe's maverick predecessor Junichiro Koizumi, but media said Koizumi had already turned down the request.

The LDP is considering choosing a new leader on Sept. 19 or 25, with many saying the party should not make undue haste.

"The (LDP) election should reflect the will of all the party members," said former party secretary-general Tsutomu Takebe, who proposed holding the party poll on or after Sept. 25.

"To turn this adversity into opportunity, we should seek candidates from a wider spectrum. This is a golden opportunity to convey the messages of candidates to the party members as well as the people."

SNAP ELECTION CALLS

While the opposition took control of parliament's upper house in the July election, the LDP and its junior partner have a large majority in the lower house, which picks the prime minister.

The next leader is likely to have to lead the LDP into the next general election for parliament's lower house.

"Whoever becomes the next prime minister, he should be temporary and the public's confidence should be gauged with ... a general election," Yukio Hatoyama, the main opposition Democratic Party's No. 2 executive, told reporters.

No poll for the lower house need be held until 2009, but some analysts say parliamentary deadlock resulting from the opposition's grip on the upper house could trigger one sooner.

Abe, 52, Japan's youngest prime minister since World War Two, reshuffled his cabinet last month to win back public approval, but a poll this week showed support stuck below 30 percent.

Abe had indicated he would step down if he failed to extend the Japanese naval mission providing refuelling in the Indian Ocean to support U.S.-led operations in Afghanistan, but the timing of his move was unexpected.

The Democrats were quick to reiterate their stance against the mission, for which enabling legislation expires on Nov. 1.

Abe took office last September with approval ratings of around 60 percent, but his support has dwindled due to lost pension records and a series of scandals that cost him five cabinet ministers, including one who committed suicide.