By Barbara Lewis

BRUSSELS (Reuters) - European leaders have decided youth unemployment and the risk of social breakdown are among the toughest challenges they face and finding solutions will be a top priority for the coming months.

In a letter released late on Friday, European Council President Herman Van Rompuy said youth unemployment was one of the most pressing issues for the 27-member European Union.

"The June European Council will be an opportunity to mobilize efforts at all levels around one shared objective: to get motivated young people back to work or education," he said, referring to upcoming summit talks.

"We must give them the guarantee that they will be either in training, further education or employment within four months of leaving school."

EU ministers agreed earlier this year on steps to ensure people under the age of 25 receive an offer of work or work-related training as part of a 6 billion euro ($8 billion)initiative on youth unemployment in the worst-hit corners of Europe.

Social unrest is rumbling and research has warned of "lost generations" of unemployed people and their children.

Van Rompuy said in his public letter preparatory work needed to be carried out, so schemes to help young people could be "fully operational" by January next year.

In Germany, policy-makers have in private expressed a concern about a lack of urgency and have thrown their weight behind bilateral deals to solve the problem.

The dominant EU state says it is experienced in dealing with unemployment and is hosting talks on July 3 in Berlin to follow up on the June EU talks.

It thinks the 6 billion euros of EU money should be spent upfront, rather over the seven years of the next multi-annual budget (2014-2020). It also has said some funds could pay for the early retirement of older people to make way for the next generation.

Van Rompuy's letter notes unemployment levels vary greatly across the European Union, underlining the case for sharing best practice.

For the European Union as a whole, unemployment is 10.9 percent and in the 17-member euro zone, it reached a record 12.1 percent of the working population in March, the latest public figures. [ID:nL6N0DH20A] In the United States it is 7.6 percent.

Among EU member states, the lowest unemployment rates are in Austria (4.7 percent), Germany (5.4 percent) and Luxembourg (5.7 percent), while the highest are in Greece (27.2 percent), Spain (26.7 percent) and Portugal (17.5 percent), according to Eurostat data issued at the end of April.

The EU jobs crisis has stoked debate on how tough economic policies need to be to fix the EU economy.($1 = 0.7734 euros)

(Additional reporting by Luke Baker; editing by Ron Askew)