Shares around the world rebounded strongly today as traders took heart from the US government's multibillion dollar rescue of Citigroup, the tottering US banking behemoth.

The move gave a big boost to confidence, sending shares sharply higher throughout Europe. The Dow Jones Industrial Average was also expected to move ahead strongly when trading begins later today. Citigroup shares surged more than 30% in pre-market trading, to $5.07.

By 1pm, the FTSE 100 index, which suffered its third worst week ever last week, was trading 176 points higher, a jump of almost 5%.

In an effort to shore up confidence in America's crumbling financial system, the US government has taken a $20bn (£13.4bn) stake in the bank. Its shares surged more than 30% in pre-market trading on Wall Street this afternoon.

The US treasury secretary, Henry Paulson, and the Federal Reserve chairman, Ben Bernanke, worked with officials throughout the weekend on the lifeline for the institution whose collapse would have wreaked havoc on the US economy.

The New York Federal Reserve board president, Timothy Geithner, who is expected to be nominated later today to succeed Paulson as treasury secretary, also was closely involved.

"With these transactions, the US government is taking the actions necessary to strengthen the financial system and protect US taxpayers and the US economy," the authorities said in a statement issued late last night. "We will continue to use all of our resources to preserve the strength of our banking institutions, and promote the process of repair and recovery and to manage risks."

The $20bn cash injection by the treasury will come from the $700bn US financial bail-out package. The move follows an earlier $25bn infusion in Citigroup for which the government received an ownership stake.

As part of the plan, the treasury and the Federal Deposit Insurance Corporation will guarantee against the "possibility of unusually large losses" on up to $306bn of risky loans and securities backed by commercial and residential mortgages.

Under the loss-sharing arrangement, Citigroup will assume the first $29bn in losses on the risky pool of assets. Beyond that amount, the government would absorb 90% of the remaining losses, with Citigroup absorbing 10%.

The agreement places restrictions on executive compensation, including bonuses, and calls on Citigroup to take steps to help distressed homeowners.

The move is the latest in a string of high-profile government bail-outs. The Fed provided financial backing to JPMorgan Chase's buyout of ailing Bear Stearns in March. Six months later, the government was forced to take over mortgage giants Fannie Mae and Freddie Mac and throw a financial lifeline to the insurance giant American International Group.

Citigroup yesterday ran full-page newspaper adverts in the US to reassure investors and creditors it could survive the latest bout of turmoil in the markets. A slump in Citigroup stock last week saw its shares lose 60% of their value.

Once the world's largest bank, Citigroup's asset base of $2tn is much larger than Lehman Brothers, whose bankruptcy in September led to a deepening of the credit crisis that was threatening to engulf Citigroup.

Citigroup is adamant that the price slump, which has pushed its stock to the lowest point since 1992, is a product of mistaken fears for the strength of its balance sheet. In its adverts, it said financial markets had been tested in "unprecedented ways" this year, but its diversified business model – which ranges from credit cards to transaction services and investment banking – would steer it through the uncertainty. It ended with a clarion call and an unintentional allusion to the exhaustive talks this weekend at Citigroup's Manhattan headquarters: "That's why now, more than ever, you can feel confident that Citi never sleeps."

Mike Mayo, an analyst at Deutsche Bank, believes reserves of $25bn and other resources should cover estimated losses of $50bn on bad loans.

Richard Bove, at Ladenburg Thalmann & Co, said it would take a repeat of the Great Depression to threaten Citigroup's survival.

However, concerns over the US economy are focusing on Citigroup. Sean Egan, at Egan-Jones Ratings, has argued that the bank might need a further $50bn. The fear is that Citigroup will be exposed to more losses if US growth deteriorates severely. Last month, the bank obtained $25bn from the treasury's troubled asset relief programme.

Vikram Pandit, Citigroup's embattled chief executive, has ruled out a break-up, dismissing reports it might sell Smith Barney, its wealth management arm. But it is understood executives have not ruled out a break-up. Market professionals said Citigroup's stock would be hammered again this morning if a deal was not struck with the US government. Joe Saluzzi at Themis Trading said it needed to announce a break-up, management change or restructuring by today. "That would probably continue a rally on Monday morning," he said.