CAIRO (Reuters) - Oil prices are starting to have an impact on the level of economic activity in the United States, but it is too early to say the economy has entered a recession, Energy Secretary Sam Bodman said on Wednesday.

"Our economy has been able to withstand the big run-up in prices but with (oil prices at) $100 (a barrel) it's starting to have an impact on the level of our economic activity," Bodman told businessmen at a lunch in Cairo.

Oil has eased from the record high of $100 struck early this month to trade around $88 a barrel on Wednesday.

Bodman said a $150 billion stimulus package for the U.S. economy was not "too little, too late" and, combined with a surprise U.S. Federal Reserve rate cut, could have an immediate impact on the U.S. economy.

Any improvement in the U.S. economy could cause a moderate increase in energy prices, Bodman said.

Bodman, in Cairo after a tour of Gulf Arab countries, said OPEC member countries would not cut supply, but it was unclear if they would boost output. OPEC next meets on February 1.

Asked if the United States would dip into its strategic oil reserves, Bodman answered: "No."