During an appearance on CBS TV’s Face the Nation program on Sunday, Rudy Giuliani did not the rule out the possibility of again running for the White House in 2012, despite an aborted Presidential bid in 2008.

I have thought about it in recent weeks,” Giuliani, said. However, he did not expand further when asked by host Bob Schieffer.

Giuliani, 66, spoke mostly about the recent massacre in Tucson, Ariz., which killed six people and wounded many others, including Arizona congresswoman Gabrielle Giffords.

Giuliani catapulted to global fame as “America’s Mayor” after the terrorist attacks of September 2001, but has fared poorly as a Presidential aspirant. During the 2008 campaign, Giuliani ignored the early primary states and focused on voter-rich Florida, thinking a victory there would push him to the top. However, he lost that state to John McCain and Mitt Romney and soon pulled out of the race.