Texas Gov. Rick Perry said on Tuesday that he is giving a second thought to mounting a presidential run, but refused to give a deadline by which he will make that decision.

Six weeks ago, this was not on my radar screen, Perry told Fox News Channel's Neil Cavuto in a live interview. But at the urging of many, his wife included, he agreed to give the race another look.

We're giving it the appropriate thought process. I'd hate to be pointing to a time specific, even if we decide to get in, he said.

Perry is the longest-serving governor in Texas history; he took office in 2000 when then-President-elect George W. Bush resigned. He also chairs the Republican Governors Association.

Perry has repeatedly denied interest in the race, and a number of Perry advisers, consequently, signed on to Newt Gingrich's campaign when he entered last month.

Last week, however, Gingrich's staff resigned in mass, further stoking speculation that Perry was building toward a run. He declined a spot in Monday's GOP debate, saying he was watching the Texas Aggies play for a spot in the College World Series.