BRUSSELS, Nov. 10 (Xinhua) -- Leaders of the European Union (EU) on Thursday urged the Greek unity government to fulfill the country's commitments to get itself out of the debt crisis.

"The agreement to form a government of national unity opens a new chapter for Greece," said a statement by European Council President Herman Van Rompuy and European Commission President Jose Manuel Barroso.

Lucas Papademos, an economist and former vice president of the European Central Bank, was appointed on Thursday to head Greece's coalition government, ending days of political deadlock in the country.

The latest progress also came after a dramatic and tumultuous week for Greece where its former Prime Minister George Papandreou had first announced and then ditched a plan for a referendum on the bailout deal offered by the EU, forcing him to resign.

The new prime minister's major task in the coming months should be implementing the bailout deal to avert a Greek bankruptcy and lead the country to early general elections.

"It is important for Greece's new government to send a strong cross-party message of reassurance to its European partners that it is committed to doing what it takes to set its debt on a steady downward path," said the statement.

While reiterating the EU's commitment to help Greece, the statement also stressed that "Greece must also do everything within its power to help itself."