* Dollar hits nearly 12-yr high vs euro, 8-yr peak against yen

* Expectations of mid-year Fed rate hike support dollar

* ECB QE program sends European yields, euro lower

* Greek concerns begin to return for euro (Recasts throughout, updates prices, adds comments; changes byline, dateline, previous LONDON)

By Sam Forgione

NEW YORK, March 10 (Reuters) – The U.S. dollar hit a fresh nearly 12-year peak against the euro and its highest level against the Japanese yen in nearly eight years on Tuesday on expectations for a mid-year Federal Reserve rate hike and the European Central Bank’s bond-buying program.

The dollar index, which measures the greenback against a basket of major currencies, hit its highest since September 2003. The euro fell to $ 1.07205, its lowest level since April 2003, before paring losses. The euro also hit 129.965 yen , its lowest level against the yen since September 2013.

“We’re seeing a generally hawkish tone out of the Fed,” said Chris Gaffney, president of EverBank World Markets in St. Louis.

“There is a real desire from the Fed to just start the process, to get rates off zero,” he said.

He cited Dallas Fed president Richard Fisher’s comments late Monday that the Fed should promptly end its easy monetary policy and press ahead with an interest rate hike, in addition to last week’s strong February U.S. jobs report.

The launch of European Central Bank quantitative easing on Monday drove European yields lower and weakened the euro.

The dollar hit 122.040 yen, its strongest level since July 2007. The greenback also hit 0.98605 franc, its highest since the Swiss National Bank scrapped a 1.20 francs per euro cap on Jan. 15.

The dollar also hit its highest against the Mexican peso since at least 1989, at 15.6218 pesos, and its highest against the Brazilian real in nearly 11 years, at 3.1722 real.

Renewed concerns about Greece’s finances also weighed on the euro. Euro zone ministers warned Greece on Monday that it had “no time to lose” in securing further funding.

“Greece is thoroughly unresolved,” said Richard Franulovich, a senior currency strategist at Westpac in New York.

The dollar pared gains against the euro and erased gains on the day against the yen, however, after Bloomberg reported on Twitter that White House Council of Economic Advisers Chairman Jason Furman said the surging dollar is a headwind for U.S. growth.

The euro was last down 1 percent against the dollar at $ 1.07450. The dollar was last down 0.06 percent against the yen at 121.085 yen. The dollar was last up 1.11 percent against the Swiss franc at 0.99690 franc.

The dollar index was last up 0.72 percent at 98.292.

(Reporting by Sam Forgione; Additional reporting by Patrick Graham in London; Editing by Meredith Mazzilli)