* Trichet says debt a problem; Greece has work to do
* ECB president warns recovery will be "chaotic"
* Strong dollar is vital to world economy
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PARIS, Jan 15 (Reuters) - Growing debt is a major problem for European governments, European Central Bank President Jean-Claude Trichet said on Friday, warning that Greece in particular faced a lot of work to put its house in order.
Speaking on France Inter Radio, Trichet said that although Europe had pulled out of recession, the recovery could be "chaotic" and inconsistent.
Asked about huge government borrowing during the crisis, Trichet said: "We have a major problem on debt (in Europe)."
He added: "On the subject of Greece, I have said it has to do its own work, in its own home so to speak. It is important work and some decisions were taken yesterday by the government."
Greece launched an ambitious three-year plan to slash its huge budget deficit on Thursday but failed to convince financial markets it can deliver on the cuts and put a swift end to its fiscal crisis. [nLDE60D1N0]
In the same interview, Trichet repeated that it was important for the global economy to have a strong dollar.
"On the euro I said, and I repeat with a lot of force, that it is very important that the dollar, as the American authorities (themselves) say ... be a strong currency which inspires confidence," he said.
Speaking a day after the ECB left its key interest rate unchanged at 1.0 percent, Trichet said the central bank would do everything necessary to keep prices under control in the medium and long term, and to create a "positive" financial environment.
He predicted modest economic growth in 2010, but warned the recovery would not be especially smooth.
"We have overcome the recession but the recovery is going to be difficult and in certain regards, chaotic. We are in a period of recovery but we must remain very prudent," he said.
He declined to give any forecast on when unemployment would stop rising, saying it was up to everyone to do what they could to help the situation. "The future is not yet written," he said.
BANKS MUST CHANGE
Turning to the banking sector, Trichet said toxic assets remained a concern, but added that the biggest problem was the additional losses accrued as a result of the economic crisis and the need to make provisions to improve bank balance sheets.
"We encourage banks to do their work. Their work is to lend to households and to companies. To do this, they need to reinforce their own balance sheets by all possible means. issuing shares when there is a market is there, to put profit aside to boost their balance sheet," he said. "We are in a period where we have to reinforce the solidity of our banks so they can do their work, which is making loans."
He also said banks would not be allowed return to their old, pre-crisis ways of rewarding staff.
He declined to describe recent bonuses for top bankers as "obscene" as U.S. President Barack Obama did on Thursday but said there was a broad consensus that pay structures in the sector had to change.
"It's clear that it will no longer be accepted by our society," he said.
However, he said bankers should not be turned into scapegoats for the crisis.
"You have to be very careful. It's the whole system which disfunctioned. The banks malfunctioned, the non-banks malfunctioned. The mechanisms that we had put in place in accounting, in agency ratings, the whole system of rules of caution, all that has proved much too fragile a system." (Reporting by Sophie Taylor and Crispian Balmer, editing by Mike Peacock)