"We would work not only with our allies, like Japan and South Korea and Taiwan. We'd work with non-aligned countries like India and Vietnam that are desperate and hungry for American leadership," 44-year-old Jindal told the Fox News.
Jindal, who last month announced his bid for the 2016 presidential elections, was responding to questions on addressing the challenges being posed by the Islamic State militant group in the Middle East.
Obama, he said, needs to tell clerics and Islamic leaders that they need to explicitly recognise the religious rights of others with different beliefs.
"Going back to foreign policy. We stand with Israel. I would make it clear to Iran, I don't care what deal this president signs, I'm not abiding by any deal unless it truly gets rid of their enrichment capacity, their enriched uranium, anytime, anywhere inspections," he said.
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Responding to a question, Jindal acknowledged that a recent story on him by a leading US daily was racial.
"I was offended by 'The Washington Post' saying as an Indian-American that you had abandoned the Indian-American community, and something to that effect. I felt that was a racial comment," the interviewer asked.
"We don't judge people by their backgrounds. We just people based on ideas, accomplishments. Look, the Democrats are about to crown Hillary Clinton right in an open contest. Let's compare our records. Let's compare our policies," he added.