* Dollar index rises to highest level in about 3 months
* Greenback firm after Friday's solid U.S. economic data
* Euro touches lowest in nearly 2 months
By Masayuki Kitano
SINGAPORE, July 20 (Reuters) - The dollar hit a three-month high against a basket of major currencies on Monday, after solid U.S. inflation and housing data supported expectations for the Federal Reserve to raise interest rates in coming months.
The greenback is coming off its best weekly performance in about two months, having risen last week after Fed Chair Janet Yellen reiterated that U.S. interest rates will probably be lifted later in the year.
The dollar gained further support from data on Friday that showed U.S. consumer prices rose for a fifth straight month in June, while housing starts jumped and building permits surged to an eight-year high. ID:nL2N0ZX0JV
Against a basket of six major currencies, the dollar last traded at 97.974 .DXY . It rose as high as 97.993 earlier on Monday, its strongest level since April 23. The dollar index rose 1.9 percent last week, its best weekly gain since May.
Against the yen, the dollar held steady at 124.12 yen JPY= , having hit a three-week high of 124.235 yen on Friday.
Yen-related trading activity is likely to be thinner than usual with financial markets in Tokyo closed on Monday for a public holiday.
The euro held steady at $1.08305 EUR= . Earlier, it slipped to $1.08275, its lowest level since late May.
The euro has struggled even though worries about Greece exiting the euro zone have waned, at least for the time being, after Athens agreed to a debt deal with its creditors last week.
The single currency has come under renewed pressure while the dollar has gained broadly, as investors shifted their focus back to the diverging outlook for monetary policies and interest rates among major economies.
"The euro's direction is probably still toward the downside," said Teppei Ino, an analyst for global markets research for Bank of Tokyo-Mitsubishi UFJ in Singapore.
In the short term, however, the market may lack fresh incentives to sell the euro further, especially with Yellen's congressional testimony out of the way, Ino said.
Greek banks are ready to open their branches across the country on Monday after a three-week shutdown, officials said, while German Chancellor Angela Merkel called for swift aid talks so Athens could also lift withdrawal limits. ID:nL1N0ZZ0FN
The euro showed little immediate reaction after Germany's finance ministry said on Monday the German economy likely grew by around 0.3 percent in the second quarter, the same pace as the January-March quarter. ID:nL5N0ZX3JD
The Australian and New Zealand dollars struggled to gain traction after hitting six-year lows last week as weakness in commodity prices crimped growth prospects in their respective economies.
The Australian dollar eased 0.1 percent to from late U.S. trade on Friday to $0.7370 AUD=D3 . On Thursday the Aussie had hit a six-year low of $0.7350, its lowest level since May 2009.
The New Zealand dollar NZD=D3 , which set a six-year low $0.6498 on Thursday, held steady at $0.6512.
The kiwi's main test this week will be Thursday's Reserve Bank of New Zealand interest rate review, with the market expecting an interest rate cut and a strong easing bias in the statement. (Editing by Richard Borsuk)