But, Bush argued, it took too long for Obama to make his first visit to a U.S. mosque as president.
"I don't think it's divisive to go speak in a mosque. I'm surprised it took his eighth year to do it," the former Florida governor told reporters after stopping at a diner here. "The bigger issue is what have you done to deal with ISIS. It's important to recognize that peace-loving Muslims who are American citizens are as American as you and I are, but at the same time, this President has been derelict in his duties to destroy the caliphate."
His comments come after Donald Trump and Marco Rubio criticized Obama for visiting a Baltimore mosque on Wednesday
, where he stressed a message of tolerance and condemned anti-Muslim rhetoric.
While Rubio acknowledged there's discrimination in America, he argued the bigger problem is radical Islam.
"I'm tired of being divided against each other for political reasons like this President's done," Rubio said Wednesday at a campaign stop in New Hampshire. "Always pitting people against each other. Always. Look at today: He gave a speech at a mosque. Oh, you know, basically implying that America is discriminating against Muslims."
Meanwhile, Trump, who's long stoked questions about Obama's religion, said in an interview with Fox News that Obama went to the mosque because "maybe he feels comfortable there."
"I think that we can go to lots of places. I don't know, maybe he feels comfortable there," Trump told Fox News' Greta Van Susteren. "We have a lot of problems in this country, Greta. There are a lot of places he can go and he chose a mosque. I saw that just a little while ago. So that's his decision, it's fine."
Bush, whose brother, former President George W. Bush, notably visited a mosque shortly after 9/11 to warn against Islamophobia, acknowledged Thursday that "discrimination in America is bad and the threat of ISIS is real."
"You can believe in both, which is why I don't criticize the President to go to a mosque and to assure people they shouldn't be discriminated against. I think that is more than appropriate as the leader of our country," he said.
With less than a week to go before the New Hampshire primary, Bush has been drawing contrasts between himself and the top three finishers in the Iowa caucuses. He's been arguing that Rubio, Trump and Texas Sen. Ted Cruz don't have the leadership skills needed for the White House.
He's particularly zoned in on the two senators in the race.
"In Iowa, one of my last events was with (Iowa Sen.) Chuck Grassley. The guy has not missed a vote for 22 and a half years, he probably has a list of accomplishments and service to the state of Iowa and to this country that's pretty real. Marco doesn't have it. He's gifted. Ted Cruz doesn't have it. He's gifted," Bush said. "I'm not saying they're not talented people. But they don't have a record of accomplishment and some people will think about that when they make the decision of who's going to be their vote on Tuesday."