The FTSE 100 and other major European stock markets rose after signs of progress in talks to avoid a "fiscal cliff" of spending cuts and tax rises that threaten to drive the US economy back into recession.
Differences over how to resolve the "fiscal cliff" narrowed significantly on Monday night, according to the report, bringing the White House and congressional Republicans closer to a budget deal.
Investors became more optimistic that a US budget deal will be struck after President Barack Obama was said to have made a counter-offer to Republicans that included a major change in position on tax hikes for the wealthy.
Hopes of a deal pushed the FTSE 100 (FTSE: ^FTSE - news) up 0.25 per cent in early trading on Tuesday to 5,926. The index is now close to its year high of 5965.58 hit in March. Frankfurt's DAX 30 (Xetra: ^GDAXI - news) index rose 0.38 per cent to 7,634.28 points and Paris's CAC 40 (Paris: ^FCHI - news) added 0.33 per cent to 3,650.07.
In its most dramatic change in position yet, the White House is reported to have backed away from its long-standing call for raising tax rates on households making more than $250,000 a year.
Mr Obama proposed leaving lower tax rates in place for everyone except those earning $400,000 and above, Reuters said, citing sources.
His move was a counter to a proposal by Republican House of Representatives Speaker John Boehner to raise tax rates on income over $1m.
While still far from Mr Boehner's proposal it further closes the gap between the two sides.
Considerable work remains as both sides now try to bridge the gaps between them and then sell a package to their respective allies in the US Congress.
Mr Obama also moved closer to Mr Boehner on the proportion of a ten-year deficit reduction package that should come from increased revenue, as opposed to cuts in government spending.
He is now willing to accept a revenue figure of $1.2 trillion, down from his previous $1.4 trillion proposal.
"Now (Other OTC: NWPN - news) that a deal looks likely to be done, a strong end to the year for equities is certainly on the cards," said Craig Erlam, market analyst at Alpari (UK), who said the FTSE 100 could rise above the psychologically important 6,000 level before year-end.
Mr Obama and Mr Boehner remained apart on the politically explosive issue of how and when to raise the government debt ceiling to permit the government to borrow more money.
Mr Boehner has proposed a one-year boost in the debt ceiling, tied to spending cuts. Mr Obama, as of Monday night, was pushing for a two-year increase, potentially a major concession that many congressional conservatives may find hard to swallow since they have used it to extract spending cuts from the White House.
Missing entirely from Mr Obama's offer was an extension of the so-called "payroll tax holiday," which comes to an end on January 1 with an immediate negative impact on wage earners.
Introduced by the US President two years ago as an economic stimulus, the tax holiday reduced an employee's share of the payroll tax from 6.2 per cent to 4.2 per cent. Because the tax supports the Social Security program, however, there have been divisions in both parties over continuing the holiday.
Because the details were incomplete and specifics vague, particularly on such issues as cutting the Medicare, the government health insurance program for seniors, it was uncertain how much resistance might come from Congress.
But Reuters reported that its source stressed that Monday's offer was by no means the final one from the White House.
The response from Mr Boehner's spokesman was also a positive signal. "Any movement away from the unrealistic offers the president has made previously is a step in the right direction," the spokesman said, emphasising that differences remain on spending levels in particular.
"We hope to continue discussions with the president so we can reach an agreement that is truly balanced and begins to solve our spending problem."
The rapid developments Monday evening put a deal realistically within reach.
Rank-and-file Republicans, however, could have trouble with the tax increases on the wealthiest Americans that are likely to be part of any deal, while Mr Obama could have a tough time selling spending cuts to his fellow Democrats.
Economists warn that going over the fiscal cliff could push the economy into recession.