* Nearly 600,000 American jobs lost in January
* Markets awaiting stimulus plan, bank rescue
* British, German industrial output plummets
* Dow, S&P rally over 2.5 pct on bailout hopes
(Adds timing of Geithner announcement, details of rescue package given to Reuters by a source familiar with plan)
By Pedro Nicolaci da Costa
NEW YORK, Feb 6 (Reuters) - Nearly 600,000 Americans lost their jobs in January, while European and Japanese firms ran into trouble, underscoring the monumental task facing governments as they look to stem the world economic crisis.
January's U.S. employment figures brought the country's total job losses in this recession to 3.6 million, the worst uninterrupted streak since World War Two. For more, see [nN06435445]
Europe was also under severe strain, with Britain's industrial output falling in December at its fastest quarterly rate since 1974. [nL6397990]
German industrial production shrank by a record 4.6 percent month-on-month in December, and the German steel industry's new orders fell by the most since World War Two in the final quarter of last year. [nL6742189]
Earlier, top Japanese bank Mitsubishi UFJ Financial Group <8306.T> booked its first-ever quarterly net loss, hit by widening bad-loan costs and losses on stock holdings. Like Toyota, it slashed its full-year forecast further. [nT318272]
Despite the blanket of bad news, markets were buoyed by hopes the U.S. Senate will pass an economic stimulus package and a new bank bailout plan.
"The economy is just falling into oblivion, and it will get worse," said Greg Salvaggio, vice president of trading at Tempus Consulting in Washington. "What this does is it puts the focus on the Senate debate. Everyone across markets is watching Washington."
A source with knowledge of the plan told Reuters on Friday it would meld offers to insure distressed assets with some direct government purchases, as well as mortgage modifications.
U.S. Treasury Secretary Timothy Geithner will detail how the administration plans to use the funds remaining in the government's $700 billion financial bailout program in a speech scheduled for noon (1700 GMT) on Monday.
Hoping for the best, investors pushed the Dow Jones industrial average <.DJI>2.7 percent higher. The S&P 500 <.SPX> jumped nearly 3 percent.
U.S. Senate Majority Leader Harry Reid said he believed the Senate would "be able to work something out" for a deal on the huge economic package sought by President Barack Obama, assuaging some concerns the measure might not make it through.
The Democratic-led Senate will try again on Friday to pass a $937 billion package even as lawmakers sought to broker a deal to trim proposed spending. [nN05403943]
The focus of rescue plans was falling primarily on the United States, which was where the turmoil began, but the suffering was worldwide.
The world's biggest automaker Toyota Motor Corp <7203.T>
A German government source said the economy probably contracted by up to 2 percent on the quarter in the final three months of last year, and was down noticeably in the first quarter of 2009.
"Conditions in the German industrial sector are deteriorating at an alarming rate," said Carsten Brzeski at ING Financial Markets.
Bank of Japan Governor Masaaki Shirakawa said slumping exports and weak share prices were taking a heavy toll on the economy and banking system there. [nT78864]
"The worsening of economic activity in the past three months has been very severe," Shirakawa told a parliamentary committee.
Japan's largest brokerage Nomura Holdings <8604.T> said on Friday it would raise up to $3.3 billion to replenish a capital base depleted by soured investments and its acquisition of parts of failed U.S. investment bank Lehman Brothers.
Canada, like its southern neighbor, also suffered its worst job losses in over three decades in January as employers cut a record 129,000 workers, pushing the jobless rate to 7.2 percent. [nN06253705] (Reporting by Pedro Nicolaci da Costa; Editing by Chizu Nomiyama)