* Greenback seen supported after US GDP backs rate rise view
* Dollar index takes breather after setting 1-week high
* Some caution toward chasing dollar/yen higher-trader
* Dollar/yen backs off from 7-week high (Updates prices, adds comments)
By Masayuki Kitano and Hideyuki Sano
SINGAPORE/TOKYO, July 31 (Reuters) - The dollar backed off from a one-week high against a basket of currencies on Friday, but was still seen on firm footing after U.S. GDP data supported the case for the Federal Reserve to raise interest rates later this year.
The dollar index last traded at 97.358 .DXY =USD , taking a breather after rising to as high as 97.773 on Thursday, its strongest in more than a week.
U.S. gross domestic product growth in the second quarter was 2.3 percent, lower than the consensus 2.6 percent forecast.
First quarter growth was revised up to 0.6 percent from an initial reading of a 0.2 percent contraction.
The report also showed a pick-up in inflation and strong consumption during the second quarter.
"The U.S. GDP was mixed but on the whole it underpins the case for a rate hike. The market will continue to search for more hints on whether it will come in September or later," said Shin Kadota, chief FX strategist at Barclays (LONDON:BARC) in Tokyo.
The data followed the Federal Reserve's cautious but upbeat assessment on the economy on Wednesday, which some traders saw as bullish for the greenback.
U.S. interest rate futures priced in a higher chance of a September rate hike, with the price of Federal Fund rate futures contracts for September to December all hitting the lowest level in a month and a half.
The euro rose 0.2 percent to $1.0947 EUR= . On Thursday, the euro had slipped to $1.08935, its lowest level in more than a week, pressured by the greenback's firm tone.
The dollar eased 0.1 percent to 123.98 yen JPY= , inching away from a seven-week high of 124.58 yen set on Thursday.
Traders were cautious about pushing the Japanese currency to 125 yen, as Bank of Japan Governor Haruhiko Kuroda had said in June that he saw no reason for further currency weakness when the yen was around that level.
"The trend of dollar strength will probably continue heading into the U.S. jobs data next week," said Shinji Kureda, head of FX trading group for Sumitomo Mitsui Banking Corporation in Tokyo. The July U.S. nonfarm payrolls data is due on Aug. 7.
Market players, however, are likely to be wary of buying the dollar actively at levels above 124.50 yen, he said.
Politically-motivated moves to curb further dollar strength and yen weakness, such as comments from U.S. and Japanese officials, might emerge when the dollar is at levels above 124 yen and even more so at levels above 125 yen, he said.
"I think you need to watch out for checks along those lines, as possible noise," Kureda said.
The yen showed limited response to mixed Japanese inflation data, which showed nationwide core CPI rose 0.1 percent in June, more than economists' forecast of a flat reading.
But July core CPI in the Tokyo area, announced one month ahead of nationwide figures, showed core CPI declined 0.1 percent. (Editing by Eric Meijer & Shri Navaratnam)