Graham expressed strong support for India, saying it's a country and region that has been off the radar for a while but deserves more attention.
"I hope that we can get to India to show solidarity," he said. "I don't think we've paid enough attention to the country. What happens there matters here."
The attacks, which killed at least 174 people, including 18 foreigners, in India's financial capital, ended Saturday when commandos killed the last three gunmen inside a luxury hotel.
Graham was joined by Democratic Sen. Claire McCaskill of Missouri on FOX News Sunday with Chris Wallace in an interview that covered the deadly terrorist attacks in Mumbai, President-elect Barack Obama's Cabinet selections and a possible bailout of Detroit's big three automakers.
"The Obama team is looking at strengthening the region and what Obama has said is that the terror threat we face is in Pakistan, not Iraq," she said.
Graham said Obama, by keeping Gates on as Pentagon chief, shows that he realizes that the Iraq troop surge strategy worked.
"The man he picked saved Iraq from chaos and he will listen to this man and his team as he tries to get us out of Iraq," he said.
McCaskill said Obama's selection of Gates and his former rival Hillary Clinton as secretary of state shows he is not afraid to be challenged.
"He wants to be challenged and that's how he finds his way to the strongest policy for the Americans," she said. "And I think his listening ability is shown by the way he is picking his Cabinet and I think America should be very proud of that."
Graham and McCaskill crossed swords over a bailout of the auto industry. The automakers will present a recovery plan Tuesday to Congress in hopes of getting a $25 billion loan. Automakers predict catastrophic consequences for the U.S. economy if they are allowed to fail.
But Graham, who acknowledged he knows "nothing" about running a car company, opposes federal intervention, stressing that the only way for the industry to fix its problems is to go through bankruptcy protection and reorganize.
"I don't think it's a good idea to give the money to them," he said. "They have a business plan doomed to fail."
McCaskill supports the bailout and wants to keep Americans working in the industry, noting that she just bought a new Chevy hybrid pickup.
"I hope people think about Santa Clause and the auto industry this Christmas," she said.