Global shares and other risk assets rose on Tuesday, encouraged by signs of a U.S. budget compromise aimed at stopping a package of tax hikes and spending cuts hurting the economy next year.

The differences over how to resolve the "fiscal cliff" narrowed significantly on Monday night when the White House proposed leaving lower tax rates in place for everyone earning under $400,000.

That was a change of position for President Barack Obama who has been pushing for a $250,000 threshold although it is still far from Republican House of Representatives Speaker John Boehner's preference of $1 million.

"Overnight news on the fiscal cliff has been taken positively by the markets here in Europe after underperforming the U.S. recently," Securequity sales trader Jawaid Afsar said.

European shares <.STOXX50E> mirrored an upward push by Asian equities, opening up 0.5 percent as London's FTSE 100 , Paris's CAC-40 and Frankfurt's DAX climbed between 0.4 and 0.5 percent.

It left the MSCI index of global stocks <.MIWD00000PUS> 0.2 percent higher, on the cusp of a three-month high and with a more significant 1-1/2 year high also in its sights.

Futures suggested a higher Wall Street opening too and oil, copper and gold also firmed. Expectations of more monetary easing in Japan kept the yen soft, however.

As European trading gather pace, the dollar inched up 0.1 percent to 83.96 yen, off a 20-month high of 84.48 yen hit on Monday but well above its late New York levels on Friday. The euro hovered at $1.3158.

Concerns that fiscal stimulus could seriously increase the country's debt burden pushed the benchmark 10-year Japanese government bond yield to a one-month high of 0.750 percent.

In European bond markets, trading remained subdued ahead of the year-end. German Bund futures slipped to 144.62 as increasing signs of progress in the U.S. budget talks eased demand for low-risk assets.

"We're lower on the fiscal cliff progress. The markets are very thin out there and so price moves could get overdone today," said one bond trader.

(Additional reporting by David Brett; William James; editing by Anna Willard)