By Francesco Guarascio

BRUSSELS (Reuters) - Germany and the European Commission told Italy on Wednesday to follow the rules after Italy made preliminary plans to prop up its banks in the wake of volatility caused by Britain's vote to leave the European Union.

Rome says it is concerned that Italian banks, which hold 360 billion euros ($400 billion) of bad loans, a third of the euro zone's total, risk attack by hedge funds betting that market turmoil could tip them into full-blown crisis.

Banking and government sources said Italy was preparing to protect its banking industry by requesting more flexibility from the EU on both public spending and state aid for its lenders.

The Italian initiative did not go down well in Germany, the main contributor to the EU budget and a staunch supporter of fiscal discipline and strict rules.

"On the banking union we established specific rules as far as the winding down of banks, the recapitalization of banks is concerned," German Chancellor Angela Merkel told a news conference after a summit of EU leaders in Brussels, the first after Brexit.

"We can't come up with new rules every two years," she said, replying to a question about Italy's requests.

Merkel's comments came after an EU official told Reuters that the Commission, which is in charge of competition policies and financial rules, stood ready to support the banking sector in Italy but did not give its backing to Rome's plans.

"The Commission is ready to help but so far it has not been convinced by what has been proposed by Italy," the official said.

EU rules allow member states to provide financial help to banks only in case of an exceptional situation.

"Can the Italians really prove that there is a systemic problem caused by the British vote? I don't know," the official said. "There is a special impact on the banks, this is true, but everyone in the world has been affected, not only Italy."

Italy's Prime Minister Matteo Renzi said he was confident that under existing rules the government would be able to ensure that citizens' bank savings were protected.

He insisted there was no emergency situation to face in the Italian banking sector and that Italy was not asking to change existing rules.

"The question of our banks is not on the agenda, no-one is asking to change the rules," he told reporters after the summit.

On Tuesday, Renzi had met Commission president Jean-Claude Juncker and vice president Valdis Dombrovskis, who takes control of EU financial services in July after British commissioner Jonathan Hill quit last week, and discussed the impact of Brexit on the Italian banking sector.

Renzi also said he believed a bank rescue fund Italy set up with private investors this year can be capitalized further.

The Atlante fund was set up to help banks raise money to boost their capital and shift some of bad debts. Two such capital hikes have already used up a large part of its firepower.

The official showed caution towards a new bank-led initiative in Italy: "The question is who will put the money in. At some point the possibility of the banking system will be exhausted. There are limits."

A Commission spokeswoman said on Wednesday that the EU executive is "closely monitoring market developments in the European Union, including in Italy".

"We are in close, regular contact with Italy as part of our normal exchanges. We have no comment on the speculations in the press on any potential specific measures," she said.

(Additional reporting by Gavin Jones and Isla Binnie in Rome, Noah Barkin in Brussels; Editing by Louise Ireland)