WASHINGTON — Senator Lindsey Graham of South Carolina said Sunday that he was considering a bid for the Republican presidential nomination, becoming the latest potential contender in an increasingly crowded field.

Mr. Graham, who was easily re-elected to a third term in November, said he had filed with the I.R.S. to create “a testing-the-waters committee.”

“I don’t know where this will go, but I’m definitely going to look at it,” he said on the NBC program “Meet the Press.”

Image Lindsey Graham Credit... Jabin Botsford/The New York Times

Mike Huckabee, a former Arkansas governor, and Senator Marco Rubio, Republican of Florida, discussed their own prospects on the Sunday television talk shows. Mr. Huckabee recently left his Fox News program, saying he would make a decision in the spring. After a failed attempt in 2008, he said he would focus on raising more money if he ran again.