* EU says United States needs to avoid "fiscal cliff"
* EU leaders reiterate want Greece to stay in euro
* Say on track with IMF reforms
* G20 summit set to seek balance between growth, austerity
By Barbara Lewis
BRUSSELS, May 26 (Reuters) - The United States and Japan need to tackle their tax issues and China must relax restrictions on the yuan as they share responsibility with Europe for restoring global economic health, EU leaders said ahead of a June summit of the G20 economies.
In a letter addressed to all 27 European Union nations, European Commission President Jose Manuel Barroso and European Council President Herman Van Rompuy said Europe was doing all it could.
"Europe has stepped up and assumed its special responsibility for securing the financial stability of the euro area and we will continue to do so," said the letter in the run up to the G20 summit in Los Cabos, Mexico.
"It is now up to all G20 members to enhance their efforts and deepen our cooperation in order to ensure a sustained global economic recovery."
In particular, it looked to the United States to avoid falling off a "fiscal cliff" - avoiding the problems that could result from tax rises and spending cuts meant to take effect at the end of the year. It also called on China to deliver reforms.
"Whilst we are firmly focused on playing our part, at Los Cabos, all other G20 partners should also recognise their responsibilities in building a sustainable recovery," the letter, made public late on Friday, said.
The United States and Japan also needed to implement "credible medium-term fiscal consolidation plans", it wrote.
"We should also call on China to continue strengthening its social safety nets, carry out further structural reforms and move to a market-determined exchange rate."
Europe's emphasis on the efforts needed from other nations follows protracted criticism it has not done enough to spur growth.
At a G8 summit earlier this month, the leading industrialised nations came down in favour of balancing austerity - as favoured by German Chancellor Angela Merkel - with U.S.-style stimulus.
An informal summit in Brussels, which ended in the early hours of Thursday, was the first following the election of Socialist President Francois Hollande in France.
It marked a shift in EU emphasis towards growth and the end of close agreement between Hollande's predecessor Nicolas Sarkozy and Merkel on debt-cutting.
Rompuy and Barroso said data had shown EU-internal imbalances were being reduced, although more needed to be done and, in this context, it referred not just to countries in deficit, but also those in surplus.
A senior official from a G20 nation, who asked not to be named, said many countries would be pushing for a better balance between fiscal adjustments and growth at Los Cabos.
"There's a view to stress the importance of measures to boost global growth, that fiscal consolidation can't be allowed to hurt growth," the official said.
The official also said countries were ready to send a "clear message of support to the euro zone and to maintain the integrity of the euro zone".
This week's informal EU summit also backed Greece staying in the single currency, while respecting its commitments. Friday's letter reiterated that message.
International Monetary Fund (IMF) Managing Director Christine Lagarde added her voice to the calls for Greece to abide by the rules. In an interview with Britain's Guardian newspaper she said Greeks had to take responsibility and pay their taxes.
"I think they should help themselves collectively," she was quoted as saying. "By all paying their tax."
Rompuy and Barroso said the EU was on track to implement IMF reforms, as part of global efforts to strengthen financial architecture.
"We will stress that the full implementation of the 2010 reforms is a critical element for boosting the legitimacy, credibility and effectiveness of the IMF," their letter said.
They added IMF members should be ready for "constructive discussions" on the review of the IMF rules on quotas, taking account of the need to improve IMF accountability, oversight and effectiveness.
Financial market reform should be another major theme for debate by the 20 leading economies, the letter said.
"The EU is well on track to have all financial reforms fully in place by 2013 and we expect our partners to move along with us," the EU leaders said.
They also urged the G20 to tackle trade barriers as another way to get the economy back on track and create growth and jobs.
"The recent surge in protectionism is a major concern and the G20 should strengthen the existing monitoring mechanism and improve on notifications and transparency," their letter said.