PARIS — Acting with urgency and unity, which had been sorely lacking, European nations… PARIS — Acting with urgency and unity, which had been sorely lacking, European nations unveiled plans Monday that could inject a mind-boggling $1 trillion into troubled banking systems whose failures have threatened to drag the world into a deep recession.

Stock markets around the globe rallied after Britain, Germany and France announced concrete steps that will dramatically reshape the world economy by guaranteeing bank loans and recapitalizing their countries’ commercial banks.

British Prime Minister Gordon Brown declared that his plan would be a ‘rock of stability.’ French President Nicolas Sarkozy said ‘audacious’ steps were the only way out of the crisis. German Chancellor Angela Merkel, a reluctant convert to the coordinated approach, said the measures would restore trust in the world markets.

After significant divisions last week that sent stock markets plunging, Monday’s action marked a moment of triumph for Brown, who spearheaded the strategy, and Sarkozy, who worked tirelessly as the president of the European Union to overcome German resistance to the idea.

‘I think Europe does now have its act together, and has its act together rather more than the United States,’ said Richard Portes, an economics professor at the London Business School. ‘I am actually quite encouraged by the progress that has been made quickly, and I think we have reason to hope that we’ve turned the corner.’

In total, European leaders are offering to pump more than $1 trillion into their banking systems. The goal is to assure investors that the banks are healthy and free up frozen lending between banks, which has been at the center of the worldwide fiscal meltdown.

In exchange for a lifeline, troubled banks must accept government oversight that, in some cases, will amount to partially nationalizing the financial institutions.

Other European nations already are falling in line. Also, after its initial $700 billion bank bailout strategy failed to reassure markets, the Bush administration is moving toward embracing Brown’s strategy as a crucial element of the U.S. approach.

On Monday, Merkel unveiled the most expensive of the European plans, a $681 billion package that will be used to guarantee bank loans and recapitalize German banks. The French version calls for the government to inject nearly $500 billion into the nation’s banks. Brown pledged to pump as much as $63 billion into England’s three largest banks.

‘To let the chips fall where they may would be the height of irresponsibility,’ Brown said. ‘It would be a failure of leadership precisely at the moment when vigorous action is needed to protect people who need that help most.’

Their approach addresses the heart of Europe’s problems: Banks are afraid to lend in a climate of panic. Because European banking is dominated by a few huge banks in each country, that poses a greater systemic risk than struggling U.S. banks do.

The U.S. crisis came about because of problems involving investment banks, which were subject to lesser reserve requirements than commercial banks were and were allowed to borrow more against those reserves. These same banks were crucial in developing complex, esoteric and unregulated financial instruments that threaten to implode and harm global finance.

The U.S. Treasury also is looking for ways to boost lending by healthy banks, the overwhelming majority of the more than 8,000 U.S. commercial banks.

Monday’s steps were the outgrowth of emergency meetings in Washington, London and Paris after a dizzying week of record stock market losses worldwide.

Faced with a second week of market panic, European leaders agreed on a plan that gives each nation an economic ‘tool box’ from which it can pick and choose.

‘The greatest risk today is not by being audacious, but by doing nothing,’ Sarkozy said.

Stock markets endorsed the approach Monday by staging strong rallies. In New York, the Dow Jones Industrial Average posted its biggest one-day point gain ever, soaring 936.42 points, or 11 percent, to 9,387.61.Germany’s DAX index ended the day up nearly 9 percent. In France, CAC stocks were up more than 7 percent. The FTSE 100 in London was up about 5 percent.

While the European nations are putting their government backing behind troubled banks, the final bill for taxpayers may not be as high as the numbers suggest.

The goal in each country will be to instill confidence in the banks and attract private investment.

‘I think this gets over the first hurdle,’ said Viral Acharya, a professor of finance at New York University and the London Business School. ‘This eliminates the complete lack of confidence, but the challenge now is for the banks to go out and find more capital on their own.’

In the most significant element of the Brown plan, the British government could end up as the majority stakeholder of the Royal Bank of Scotland. If, as expected, RBS can’t raise enough private investment to stabilize, the British government will inject as much as $33 billion into the bank in exchange for nearly 60 percent of its stock.

Britain also could pump nearly $30 billion into Lloyds TSB and HBOS, two U.K. banks that are in the process of merging. In return, Brown’s government would receive a 40 percent stake in the bank.

‘The government cannot just leave people on their own to be buffeted about,’ Brown said in announcing the plan. ‘We must, in an uncertain and unstable world, be the rock of stability upon which people can depend.’