* Stocks push higher after upbeat U.S. factory data
* Dollar firms versus yen, euro steady
* Ukraine's hryvnia firms on prospect of deal to end crisis
LONDON, Feb 21 (Reuters) - Shares and the dollar rose on Friday, buoyed by upbeat U.S. factory activity data the previous day, while Ukraine's currency and bonds firmed on prospects of a deal to end a crisis that has killed 75 people in two days.
European stocks pushed higher, following gains in Asia and on Wall Street, after Markit's flash U.S. Manufacturing Purchasing Managers Index on Thursday hit its highest since May 2010, easing investor worries over recent data suggesting the economy was stuttering.
"It is a positive sign that the U.S. economy is improving," David Battersby, investment manager at Redmayne-Bentley, said. "And if the economy is improving, then they will be sucking in imports. Things are getting back on track."
The data helped push the dollar higher against the yen though the euro held steady to the U.S. currency after a similar measure of euro zone activity on Thursday came in below forecast and the French services sector contracted.
The overall positive tone in markets nudged U.S. Treasury yields higher, with 10-year bonds yielding 2.76 percent, compared with 2.75 percent in late U.S. trade.
However, German 10-year yields, the euro zone benchmark, fell 2.7 basis points to 1.67 percent as investors focused on the patchy European numbers.
"There's still a lot of uncertainty about the state of the global economy. The China and euro zone PMI data wasn't particularly great and that leaves the door open for ECB action," said Alan McQuaid, chief economist at Merrion Stockbrokers.
In Ukraine, the hryvnia currency rose to 8.83 per dollar, lifting off a five-year low of 9.085 on Thursday. Its dollar bond prices rose and debt insurance costs fell.
The presidency said a deal had been reached to end the crisis but the opposition did not immediately confirm agreement had been reached and there were still reports of fighting in Kiev.
Standard and Poor's cut Ukraine's credit rating for the second time in three weeks, lowering it by one notch to triple-C and saying there was an increased risk of default.
Neighbouring Russia's rouble firmed to 41.66 against the dollar-euro basket, off record lows set on Wednesday.
Most Asian emerging market currencies rose on Friday as the U.S. numbers boosted appetite for risk.
MSCI's all-country world equity index, which tracks shares in 45 countries, rose 0.3 percent. The FTSEurofirst 300 index of top European shares gained 0.3 percent to 1,343.36 points.
Earlier Japan's Nikkei index closed 2.9 percent higher and MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.83 percent.
On Wall Street, the S&P 500 ended up 0.6 percent on Thursday. The U.S. stock market has largely pinned recent weak data on the impact of extremely cold weather rather than worsening fundamentals.
"The market thinks for now that underlying U.S. economic trend remains strong and things will get better in the spring, when it gets warmer," said Sho Aoyama, senior market economist at Mizuho Securities.
MSCI's main index of emerging markets stocks was up 0.7 percent, reversing a fall on Thursday when data showed Chinese factory activity contracting.
The Chinese yuan fell to 11-week lows as the central bank was seen pushing the yuan weaker in a likely prelude to widening its trading band and as emerging market currencies weaken.
The dollar rose against a basket of currencies and formed 0.2 percent against the yen, which last traded at 102.40 to the greenback.
The euro was steady at $1.3710, having hit a seven-week high of $1.37735 on Wednesday.
Market participants were also watching for developments from this weekend's Group of 20 meeting of finance ministers and central bank chiefs in Sydney, at which global growth and recent turmoil in emerging markets are expected to be in focus.