Washington (CNN) Donald Trump seemed to suggest that President Barack Obama had an ulterior motive concerning how he addresses and handles terror attacks, because he does not say the phrase "radical Islamic terrorism."

"We're led by a man who is very -- look, we're led by a man that either is not tough, not smart, or he's got something else in mind. And the something else in mind, you know, people can't believe it," Trump said Monday morning on Fox News' "Fox and Friends."

"People cannot believe, they cannot believe that President Obama is acting the way he acts and he can't even mention the words 'radical Islamic terrorism.' There's something going on. It's inconceivable. There's something going on."

Asked earlier why he had tweeted that Obama should resign because he wouldn't say the phrase "radical Islamic terrorism," Trump said, "He doesn't get it or he gets it better than anybody understands. It's one or the other, and either one is unacceptable."

Later in the day, White House spokesman Josh Earnest told reporters he hasn't spoken with the President about what Trump had said, but he added, "When you are focused on something as big as helping the country respond to the worst mass shooting in our nation's history, when you are focused on something as big as safeguarding the country and combating violent extremism, it's important not to get distracted by things that are so small."

Read More