* European bourses rise as black boxes handed over
* Russian stocks see first rise in almost two weeks
* MSCI Asia hits 3-year peak, Nikkei up after Japan holiday
* U.S. stock futures edge higher, underpinned by earnings
* Dipping U.S. Treasury yields still hold back dollar
LONDON, July 22 (Reuters) - European markets rode a global rebound in risk appetite on Tuesday helped by the first signs of cooperation from Ukraine's pro-Russian separatists over the downed Malaysian Airlines plane.
After days of uncertainty, a train carrying the remains of some of the almost 300 victims was heading for Ukrainian government territory and flight recorders had been passed to Malaysian authorities by separatist leaders.
It helped settle the recent market nerves, lifting shares both in Europe and Asia and pushing back many safe-haven assets like the yen, gold and government bonds that have been in demand over the last week.
Europe's FTSEurofirst 300 index was up 0.7 percent as the main bourses in London, Frankfurt and Paris all climbed, while dollar-traded Russian stocks in Moscow saw their first rise in almost two weeks.
The rouble also firmed, trading 0.5 percent stronger against the dollar at 35.03 and the euro at 47.36 .
"The separatists have reportedly met several of the key demands coming from Malaysia and Western countries," Sberbank Investment Research analysts said.
The dollar crept up 0.1 percent to 101.48 yen, having pulled back from a low of 101.09 hit late last week, while gold dipped about two dollars to $1,305 an ounce.
The rebound in risk was also aided by more solid U.S. company earnings and merger activity in the previous session, though analysts remained wary about Ukraine and Russia given the delicate situation.
EU foreign ministers gather later in the day in Brussels to discuss the events and possibly recommend further sanctions against Russia. Russia's Security Council, headed by President Vladimir Putin, is also due to meet in Moscow.
In Asian trading, MSCI's broadest index of Asia-Pacific shares outside Japan rose about 0.7 percent to be at its highest since 2011.
"Investor sentiment has settled as the VIX has stayed calm," Amundi Japan equity research and strategy department chief economist, Akio Yoshino, said.
In the Gaza Strip the Palestinian death toll jumped to more than 500 and Israeli losses rose to 29. The United States stepped up efforts to secure a ceasefire but hopes remain slim.
The yield on the benchmark 10-year U.S. Treasury note stood at 2.478 percent in European trading, not far from its U.S. close of 2.475 percent.
The yield on the 30-year Treasury bond inched down to 3.262 percent from its U.S. close of 3.264 percent on Monday, when it fell as low as 3.249 percent, the lowest since June 2013.
Investors were also awaiting U.S. consumer prices data due at 1230 GMT for clues to the timing of monetary tightening by the Federal Reserve.
The Labor Department is expected to report that U.S. inflation eased slightly to 0.3 percent in June, after rising food prices pushed the index to its biggest increase in more than a year in May.
"It will be interesting to see how euro dollar trades into the CPI numbers," Saxo Bank head of FX strategy, John Hardy, said.
"If it's higher than expected, is it dollar positive on the view that it pulls the Fed guidance forward on the first rate hike? Or is dollar negative because the Fed is seen being complacent on inflation and behind the curve?"
The euro was largely steady at $1.3524, holding above a five-month low of $1.3491 touched on Friday.
(Additional reporting by Lidia Kelly in Moscow and Lisa Twaronite in Tokyo; Editing by Louise Ireland)