* Dollar edges down from 3-year highs, tracks dip in U.S. yields * Dollar tipped for more gains on Fed stimulus scaleback, economy * Euro supported by Greek aid disbursement By Anooja Debnath LONDON, July 9 (Reuters) - The dollar tracked U.S. treasury yields down from multi-year highs on Tuesday, but investors anticipated more gains for the currency as the U.S. economy picks up and its central bank scales back monetary stimulus. Expectations the Federal Reserve, which releases minutes of its June meeting on Wednesday, will reduce its bond-buying as early as September should keep the dollar buoyant, with strategists saying its rapid recent ascent could see some corrections now but buyers would emerge at lower levels. The dollar index, which measures the U.S. currency's value against a basket of currencies, was down 0.1 percent at 84.186 , closely tracking a dip in U.S. treasury yields from a near two-year high of 2.755 percent reached on Monday. Also on Monday, the dollar index touched a three-year peak of 84.588 following Friday's upbeat U.S. jobs report. Likely modest declines in the dollar in coming days "will provide a renewed buying opportunity as the overall picture is positive for the dollar," said Ian Stannard, head of European FX strategy at Morgan Stanley. He said Wednesday's FOMC minutes would be scrutinised for any hints monetary stimulus could be tapered soon, which would support the dollar. The euro was flat at $1.2873, staying above the seven-week trough of $1.2806 hit on Friday. The single currency found some support after Greece was aid that will prevent it from defaulting on debt in August. But with the Fed poised to unwind its stimulus, while the European Central Bank looks set to keep interest rates at record lows, the euro is likely to remain under pressure. "Whatever the short-term price fluctuations... this monetary policy divergence will drive euro lower over the medium term," analysts at Societe Generale said adding that they were short euro versus the dollar, sterling and the Norwegian crown. The dollar is also expected to rise against the yen and sterling as the Bank of Japan is expected to continue with its aggressive monetary stimulus, while the Bank of England has indicated it was in no hurry to hike rates. Against the yen, the dollar rose 0.2 percent to 101.17 yen , off a near six-week high of 101.54 yen on trading platform EBS hit on Monday.