By Koh Gui Qing and Langi Chiang

BEIJING (Reuters) - The top candidate to run the International Monetary Fund, French Finance Minister Christine Lagarde, said she backed a bigger say for China at the Fund while making clear that the euro zone crisis would be a priority if she wins the job.

Lagarde made the comments in Beijing, the latest leg of her world tour to seek support for her IMF candidacy. She is seen as the favorite to replace former IMF chief Dominique Strauss-Kahn who was arrested last month on sexual assault charges.

Lagarde said her talks with Chinese central bank and finance ministry officials about her candidacy were positive, but she stopped short of claiming Beijing's outright support.

"I'm very positive about my trip to China but the decision does not belong to me. It belongs to the Chinese authorities," she told a news conference at the French embassy in Beijing.

"I'm confident, I'm very positive about the meetings I've had so far. Some governments and some countries have decided to go public early. My sense is that it's too early to count your chickens if I may say."

China has not spelt out whether it supports Lagarde, but it has joined other big emerging economies in demanding that the IMF and other international financial institutions give greater heed to their demands.

And in Beijing, Lagarde indicated she was listening to those demands. She said she backed the decision to increase China's voting rights at the IMF from 3.65 percent to 6.4 percent, and also said the organization would help Beijing internationalize its yuan currency.

After her talks with Chinese Vice Premier Wang Qishan and central bank chief Zhou Xiaochuan on Wednesday, Lagarde hinted that there was room for more reforms at the IMF to give rising economies more say.

"The second thing that we also agreed on was that the trends of reforms that has taken place must be continued and must be developed, both in relation to the governance of the fund, in relation to the appropriate representativeness of its members, particularly with those countries that are underrepresented, as is the case with China," she said.

But Lagarde also made clear, however, that her priority if she becomes managing director of the IMF will be the euro zone crisis that continues to threaten Greece, Portugal and other European economies struggling to cut gaping fiscal deficits.

"Clearly, it is the immediate focus of the Fund's operations at the moment," she said of the euro crisis.

She urged Greece to emulate Portugal in seeking to form a broad political alliance to push through painful reforms.

Portugal's prime minister in waiting, Pedro Passos Coelho, has begun formal coalition talks with the rightist CDS-PP party to seek a pact to form a majority government.

"One great strength of Portugal which I hope Greece will be able to emulate is that Portuguese political parties and authorities joined forces and formed an alliance. That was critical," said Lagarde.

India's Finance Minister Pranab Mukherjee said on Tuesday that the country had not committed to supporting Lagarde's bid despite her visit, a sign that India may still be hopeful of nominating an alternative candidate.

The main obstacle in Lagarde's bid for the top IMF job is the possibility of an inquiry into her role in a 2008 arbitration payout.

Mexico's central bank chief Agustin Carstens, who is also competing for the IMF job, is due to visit China next week.

(Writing by Kevin Yao; Editing by Ken Wills)