* Dollar lower on bullish European data
* Yen gains on Ukraine tensions
* Dollar index hits lowest in more than six months (Adds comments and updated prices)
By Sam Forgione
NEW YORK, May 6 The dollar slid to an eight-week low against the euro on Tuesday on bullish European data and a growing belief that the dollar is showing reluctance to respond to positive U.S. economic news, while tensions in Ukraine drove demand for the safe-haven yen.
The euro was helped by strong surveys of service-sector purchasing managers in Spain and Italy. It remains supported by flows of capital into its southern economies, where interest rates on government debt are still much higher than those in the United States.
A fall in euro zone inflation halted last month and the PMI surveys of service-sector purchasing managers made for a bullish reading on the prospects for a strengthening of the southern economies most hurt by four years of turmoil over government debt.
"The data suggests that activity in the euro zone could be improving, and that was positive for the euro," said Eric Viloria, currency strategist at Wells Fargo Securities in New York.
Data also showed the U.S. trade deficit narrowed in March as exports rebounded. March's shortfall, however, was a bit bigger than the $38.9 billion that the government had assumed in its advance first-quarter gross domestic product estimate published last week.
"The March deficit was bigger than people had factored into their first-quarter GDP numbers," said Steven Englander, global head of G10 FX strategy at CitiFX in New York.
He also said that the dollar's weak response to positive U.S. jobs data on Friday was a sign of the dollar's failure to rebound. The dollar reaped short-lived gains on Friday after news of surprisingly strong hiring that took the U.S. unemployment rate in April to a 5-1/2-year low.
"The bar for good news to take the dollar up seems to be pretty high," Englander said.
The U.S. dollar index, which measures the dollar against six major currencies, fell on Tuesday to 79.06, its lowest in more than six months.
Traders said persistently low U.S. interest rates, which have remained at current levels partly on the belief that the Federal Reserve will not raise rates soon, have hurt the dollar.
Ongoing clashes in Ukraine, meanwhile, drove buying in the safe-haven yen. Pro-Russia rebels shot down a Ukrainian helicopter in fierce fighting near the eastern town of Slaviansk on Monday, while Kiev moved police special forces to the port city of Odessa to stop the rebellion spreading westward.
The yen also gained on weakness in equities. On Wall Street, the benchmark S&P 500 lost 0.77 percent as disappointing earnings from AIG weighed on financial shares.
The euro was last up 0.39 percent against the dollar at $1.393, while the dollar was down 0.49 percent against the Japanese yen at 101.61. The dollar was also down 0.44 percent against the Swiss franc to trade at 0.8739 francs.
The dollar index was last down 0.48 percent at 79.108.
The Russian rouble, meanwhile, gained after data on Tuesday showed Russia's inflation rate increased to 7.3 percent in April from 6.9 percent in March, raising the likelihood that the Russian central bank will raise interest rates, said Wells Fargo's Viloria.
The dollar was last down 0.94 percent against the rouble to trade at 35.39 roubles. (Reporting by Sam Forgione, additional reporting by Patrick Graham in London; Editing by Chizu Nomiyama; and Peter Galloway)