By Lucia Mutikani

NEW YORK (Reuters) - The dollar fell on Friday and was on track for its steepest weekly decline against a basket of major currencies in two months, as investors worried surging oil prices could deepen an economic downturn and fan inflation pressures.

Investors shrugged off data showing a sharp fall in euro zone services activity in May and a slowdown across German's manufacturing sectors, convinced that boiling oil prices may even force the European Central Bank to raise interest rates this year.

Also weighing on the dollar was news that the stock of unsold U.S. houses touched a record high in April, indicating that the housing market rout was far from over.

"It just goes back to negative U.S. dollar sentiment that has been developing in the last while," said Stephen Malyon, senior currency strategist at Scotia Capital in Toronto.

"The services report didn't appear to hurt the currency. The market is more concerned about crude oil and the weakness in the dollar."

The euro climbed to a session high of $1.5794 and last traded up 0.3 percent at $1.5783, off a one-month high of $1.5814 touched on Thursday. On the week, it rose 1.2 percent, the most since March.

The dollar fell 0.8 percent to 103.25 yen. The New York Board of Trade and Industry's dollar index .DXY, which tracks the dollar's performance against a basket of major currencies, was down 1.2 percent on the week. If that holds, it would be its biggest weekly decline since late March. The index was last down 0.3 percent at 71.943.

Volume on Friday was light, with both the United States and Britain heading into long holiday weekends. The euro was also boosted by a report showing Belgian business confidence, a bellwether for the euro zone, rebounded in May.