* Tougher issues such as euro zone budget put off for now
* Germany and France to agree on a vision by March
* Reforms intended to make euro zone more resilient
* Joint bank deposit protection under discussion (Releads with final press conference, German, French, Dutch comments)
BRUSSELS, Dec 15 (Reuters) - European Union leaders on Friday set the completion of a banking union and expansion of the role of the euro zone bailout fund as priorities for euro zone integration, putting off contentious issues such as a budget for the currency area.
"In the next six months, the work of our finance ministers should concentrate on areas where the convergence of views is the biggest," summit chairman Donald Tusk told reporters after a summit of the 27 countries that will remain in the EU after Britain leaves in 2019.
"Progressing step-by-step on ... the completion of the banking union and the transformation of the ESM into the so-called European Monetary Fund should significantly strengthen the resilience of the Economic and Monetary Union," he said.
Tusk said discussions would continue on other ideas such as a euro zone budget, finance minister, parliament or sovereign insolvency mechanism, but they needed more time to "mature".
These are issues where there are wide differences between the key players -- French President Emmanuel Macron, German Chancellor Angela Merkel and European Commission President Jean-Claude Juncker.
At a joint press conference to underline Franco-German cooperation, which has traditionally driven EU development, Merkel and Macron said they would have a joint view on euro zone reform by March, when EU leaders meet again on the issue.
"There is agreement that we aim for a banking union. There is agreement ... that there will be structural reforms," Merkel told reporters.
The aim of the reforms is to protect the 19 countries using the euro better from financial crises and help rally the EU around it at a time of strong anti-EU sentiment and Britain's decision to leave the EU.
Strengthening the banking sector by gradually introducing a pan-European scheme to protect bank deposits across borders is one of the ideas that enjoy broad support, although with caveats.
"We want the debate to focus mainly on the banking union," Dutch Prime Minister Mark Rutte told reporters. "But the banks must first be made safe ... before you go to deposit guarantees."
Germany and the Netherlands insist that the deposit guarantees can only become reality when risks in the banking sector are substantially reduced.
This is likely to mean cutting the number of bad loans that banks hold, and adjusting the risk weighting on government bonds to better reflect the likelihood of sovereign default.
The other idea that the leaders back is to transform the euro zone bailout fund, the ESM, into a European Monetary Fund and make it an emergency backstop for the euro zone's bank resolution fund -- an idea tested since 2013.
The new fund would handle all future bailouts, cutting out the International Monetary Fund, which has clashed with euro zone governments over debt relief for Greece in connection with its latest bailout.
But at the heart of the debate are more contentious issues, such as creating a post of finance minister for the euro zone and a budget that could finance shared European public infrastructure or be a buffer against external shocks.
Macron said earlier this year he wanted a euro zone budget of several hundred billion euros, while Berlin wants no budget at all. In an effort to bring the positions closer, Macron stressed on Friday that in his main policy speech in September he did not mention a numerical value for the budget.
"The size will be determined by our ambition and ability to develop a common vision," Macron said, standing beside Merkel.
Siding with Germany, Rutte said healthy national finances were the best protection against external economic shocks and that there was no need for a special euro zone budget.
"I am not in favour of one big European shock absorption fund, but 19 smaller ones, these being the countries themselves and their ability to deal with crises individually," Rutte said. (Additional reporting by Luke Baker, Noah Barkin and Francesci Guarascio; Reporting By Jan Strupczewski; Editing by Kevin Liffey)