World financial markets soared Thursday after the European Union approved a plan to cut Greece's debt in half and significantly increase a bailout fund designed to contain the eurozone debt crisis.

The Paris stock exchange jumped more than 6 percent, with the Frankfurt market advancing more than 5 percent. The London exchange closed up nearly 3 percent, and U.S. indexes were all ahead by about 3 percent at the close of the trading day.

European leaders generally expressed optimism regarding the results of their summit in Brussels, saying the threat to the stability of the eurozone has been contained. French President Nicolas Sarkozy said the plan was an ambitious and credible response to the crisis. German Chancellor Angela Merkel called the deal an overall good package for the next stage, but warned there were more stages to go.

Greek Prime Minister George Papandreou said the 50 percent write-off makes the Greek debt sustainable.

U.S. President Barack Obama welcomed Europe's new debt plan and said it is crucial that it be implemented fully and decisively. Mr. Obama said he has confidence in the European leadership and that the deal will definitely have an impact on the United States.

Mr. Obama spoke at the beginning of an Oval Office meeting with Czech Prime Minister Petr Necas.

In a statement earlier Thursday, the U.S. president called the agreement a “critical foundation” to help solve the eurozone crisis and said the United States will support its European allies to address global economic problems.

Following 10 hours of tense negotiations in Brussels, EU leaders said they had convinced banks and investors to accept a 50 percent loss on Greek government bonds, effectively reducing Greek debt by $140 billion. At the same time, the banks are required to raise an additional $148 billion by June. The 17-nation bloc that uses the euro currency is increasing the firepower of its bailout fund to $1.4 trillion to cover future assistance for debt-ridden nations.

The deal still leaves Greece with a significant debt burden — estimated at 120 percent of its economic output in 2020, down from 160 percent now. But Greek Finance Minister Evangelos Venizelos said that debt level “becomes viable” for the country.

Financial analysts and world leaders outside Europe have said in the past that the continent's leaders were too timid in dealing with the crisis. International creditors have approved single bailouts for Ireland and Portugal and two for Greece. Those bailouts failed to calm the fears of financial markets that Greece would eventually default on its obligations, and that the debt contagion would spread to bigger European economies in Italy and Spain.

Analysts said Thursday the Brussels agreement could give the continent's weaker economies more time to grow and adapt to the austerity measures their governments have imposed.