* Dollar index steady, just off highest since mid-Sept
* Growth concerns weigh on European markets
* Fed says in no rush to raise rates but upgrades view on economy
* Madrid shares hit after Argentina defaults again
LONDON, July 31 (Reuters) - Doubts about the health of Europe's economy dominated trade on its major stock markets on Thursday after a cautious message from the U.S. Federal Reserve did little to stem the dollar's charge to 10-month highs.
A steady rise for the U.S. currency is the central story for global financial markets so far this month and a jump in U.S. economic growth reported on Wednesday extended the dollar's gains against the euro to 6 cents since early May.
U.S. growth of 4 percent in annualised terms in the second quarter came at a time when poor company results and concerns over a still escalating situation in Ukraine have added to worries that Europe will take far longer to recover.
Euro zone inflation numbers on Thursday are expected to add to those doubts, and the pan-European FTSEurofirst 300 index was 0.2 percent lower in a choppy opening.
"Despite some decent earnings from a number of blue-chips, the market is stuck in a range, with a number of negative catalysts including Argentina's default at the forefront of investors' minds," said Lionel Jardin, head of institutional sales at Assya Capital, in Paris.
The euro was holding steady just below $1.34 after a rough ride this week that has seen it fall to its lowest since November.
Currency traders said the inflation numbers - expected to show annual price growth of just 0.5 percent in the bloc - might provide the fuel for more sales but that any move might be capped ahead of another round of major U.S. figures on Friday.
"Meagre inflation readings will underline the case for loose monetary policy for a very extended period of time," analysts from Dutch bank ING said in a morning note. "This would add to the negative sentiment behind the euro but given the scale of softness this week already, downside may be only modest."
London's FTSE was the only major European market to buck the trend, with the oil and gas sector lifted by rising profits that included a 33 percent improvement for Royal Dutch Shell, the index's biggest stock.
While the prospect of a solid U.S. recovery gave equities some general support, many Asian shares slipped on profit-taking after making hefty gains since the middle of this month.
MSCI's broadest index of Asia-Pacific shares outside Japan dipped 0.3 percent but was still not far from a 6 1/2-year high hit on Wednesday.
The Nikkei average rose 0.3 percent while Australian shares inched up to six-year highs.
Argentina defaulted for the second time in 12 years overnight after hopes for a last minute deal with holdout creditors were dashed.
Traders said that helped fuel weakness in Spanish shares, with Madrid's main index down 1.3 percent.
But the broader global impact of any default is likely to be limited because Argentina has been effectively shut out of financial markets since its 2002 default. (editing by John Stonestreet)