Bush, who apparently was taken off a stage in Philadelphia where he was making a speech, said he was not informed on the resolution and was "not familiar with the phrasing."
"I'm familiar with it. You can't vote in favour." Olmert claimed telling the US president.
"He [Bush] gave an order to the secretary of state and she did not vote in favour of it, a resolution she cooked up, phrased, organised and manoeuvred for," Olmert said.
The Israeli PM described Bush as an "unparalleled friend" of Israel.
Fourteen of the Security Council's 15 members supported the resolution, which has until now failed to stop Israel's operation in Gaza.
Olmert criticised the UN resolution, saying that "no decision, present or future, will deny us our basic right to defend the residents of Israel".
Israel launched its offensive on December 27, in what it said was an attempt to stop Hamas firing rockets into southern Israel from Gaza.
After a first week of intense air campaign, Israel sent ground forces into Gaza in the second week of fighting and is now making its deepest push into the Strip.