WASHINGTON — Europe's $1 trillion rescue package for its weakest countries sent battered financial markets rebounding dramatically worldwide yesterday on hopes that the plan would avert another global economic crisis.

The massive loan package hashed out over the weekend by the European Union and the world's major central banks reassured investors by giving Greece, Portugal and other debt-ridden eurozone nations a new credit lifeline.

Major European stock markets rocketed higher, some more than 10 percent for the day. U.S. stocks also posted steep gains, with the Dow Jones industrial average soaring about 405 points, or nearly 4 percent, to 10,785.14.

"Clearly, Brussels, Berlin and Paris are hoping this will buy a lot of time — years as opposed to weeks and months — so weaker (countries) can get their financial houses in order," said Razeen Sally, co-director of the European Center for International Political Economy in Brussels.

But Sally and others cautioned that governments and central banks once again are fighting a problem rooted in debt by taking on more debt, just as they did by funding the bailouts of their economies and financial systems during the credit-market meltdown of 2008 and early-2009.

The global economy "remains weak and highly uncertain," Sally said. "And the biggest cloud hanging over it is the massive increase in public indebtedness on both sides of the Atlantic."

Now, with fresh commitments to lend huge sums to struggling borrowers, "It does seem like you're just giving the addict another fix," said Paul Kasriel, chief economist at Northern Trust Co. in Chicago.

But Kasriel and other analysts said policymakers had little choice. With last week's plunge in global markets — including one of the wildest trading sessions in Wall Street history — it was clear that Europe's government-debt woes posed a growing threat to the world's nascent economic recovery.

Significantly, the U.S. threw its weight behind the eurozone rescue, primarily via the Federal Reserve's decision to open new credit lines with the European Central Bank. That will allow the ECB to funnel needed dollars into the euro-zone banking system.

"Last Thursday brought it home for the U.S.," said Drew Matus, an economist at banking firm UBS, referring to the computer-driven plunge of more than 700 points in the Dow index in the space of a few minutes.

A few months ago the fear had been that cash-strapped Greece might default on its debts. But in recent weeks markets increasingly began to treat Portugal and Spain as pariahs, too, driving up both countries' borrowing costs in the bond market and thereby devaluing their outstanding bonds.

Last week the talk on Wall Street was stresses were rising in the European banking system. The eroding value of government bonds put banks in Europe and worldwide at risk because financial institutions hold huge amounts of that debt.

Under terms of the rescue package, the European Union will create a separate financial entity to borrow up to $640 billion, as needed, for loans to member countries. The debt would be guaranteed by all 16 euro-zone countries.

Additionally, the International Monetary Fund pledged $321 billion in loans, bringing the aid package total to about $960 billion.