The Indian-American Louisiana Governor was talking to reporters at the White House after his meeting with Obama along with other members of the National Governors Association on Monday.
Obama is "unfit to be commander in chief," he said.
"I take no joy in saying that. I don't say so for partisan or ideological reasons," 43-year-old Jindal said in response to a question from a White House reporter.
The Louisiana Governor alleged that Obama has repeatedly refused to call the enemy "radical Islamic terrorists," and is also not willing to rule out ground troops, except for very limited missions. The President is not leading the US to victory over a brutal enemy, Jindal told reporters.
In fact, Jindal was not among the Governors who were scheduled to speak to the media after their meeting with Obama, but several questions were addressed to him.
"This is a war against radical Islamic terrorism," he said. "I think, the President loves our country. But many of us are concerned about President’s unwillingness to identify and take on directly the threat of radical Islam."
Jindal also criticised Obama’s proposed Authorization for Military Force by place a three-year timeline with the stipulation of no ground troops.
"Whether there are plans to use ground troops now or not, I think our commanders need to have the tools they need to defeat the radical Islamic terrorist that threaten us. I’d like to take out the three-year timeline. The real timeline should be, we are done when we have hunted down and have killed these terrorists," he said.