NEW YORK — Stocks rocketed higher today after European leaders agreed to a nearly $1 trillion rescue plan to avoid a major debt crisis and the U.S. Federal Reserve said it would also provide loans overseas.

The Dow Jones industrial average rose about 400 points. The Dow and broader stock indexes rose more than 3 percent. Markets also barreled higher in Europe.

Interest rates rose in the bond market after demand for Treasurys fell.

The 16 countries that use the euro and the International Monetary Fund have agreed to create a nearly $1 trillion rescue fund to support European nations burdened by heavy debt. Markets around the world plummeted last week as fears escalated that Greece’s debt problems would spread throughout Europe and upend a global economic recovery.

Investors also feared that if Greece didn’t get a bailout, the fate of the euro, which is used by 16 countries, could be in trouble. The euro rose today against the dollar.

“Europe has unequivocally said, ‘We will defend the euro’s integrity,’ ” said Oliver Pursche, executive vice president at Gary Goldberg Financial Services in Suffern, N.Y.

Pursche noted the actions taken don’t mean European leaders will ensure its current value, but that they will do what is necessary to ensure its existence.

The U.S. Federal Reserve and other central banks also stepped up with financial support to help head off what some analysts believe could have been a broader financial crisis.

The Fed reopened a program launched in 2008 during the credit crisis under which dollars are shipped overseas through the foreign central banks. Those central banks can then lend the dollars out to banks in their home countries.

Aside from the Fed, other central banks, including the Bank of Canada, the Bank of England, the European Central Bank, the Swiss National Bank and the Bank of Japan are also involved in the dollar swap effort.

In midmorning trading, the Dow rose 397.45, or 3.8 percent, to 10,777.88. The Standard & Poor’s 500 index rose 46.85, or 4.2 percent, to 1,157.73. The Nasdaq composite index rose 104.20, or 4.6 percent, to 2,369.84.

Stocks were incredibly volatile at the end of last week as investors shrugged off signs of an improving U.S. economy and focused on European sovereign debt problems. The Dow fell 5.7 percent last week to erase its gains for the year, while broader indexes fell even further. On Thursday alone, the Dow was down nearly 1,000 points late in the day before recovering some of those losses.

Stocks have dropped four straight days as triple-digit Dow moves have again become the norm. As the credit crisis grew in late 2008 and the market bottomed in early 2009, big swings were normal.

In recent months, however, the Dow had been climbing slowly and steadily in recent months on repeated signs the economy was recovering.