Trump made the comments in an interview with ITV's "Good Morning Britain" host Piers Morgan, when asked to respond to criticisms made about him by British politicians.
Asked about Cameron's remarks, Trump said he didn't care, but then added, "It looks like we're not going to have a very good relationship. Who knows, I hope to have a good relationship with him but it sounds like he's not willing to address the problem either."
He continued: "Number one, I'm not stupid, okay? I can tell you that right now. Just the opposite. Number two, in terms of divisive, I don't think I'm a divisive person, I'm a unifier, unlike our president now, I'm a unifier."
A spokeswoman for Cameron said he had made his views on Trump's "Muslim ban" proposal clear and had "nothing further to add."
The prime minister would "work with whoever is the president of the United States and he is committed to maintaining the special relationship," the spokeswoman said.
Trump: Khan doesn't know me
Trump also had words for Sadiq Khan, who became the first Muslim to hold the office of mayor of London when he was elected earlier this month.
Shortly after taking office, Khan criticized Trump's views of Islam as ignorant
-- remarks that Trump said had offended him. The new mayor had been responding to a suggestion from Trump that he would make an "exception" to his proposed "temporary Muslim ban" for Khan.
"Let's take an I.Q. test," Trump said Monday, adding that Khan had never met him and "doesn't know what I'm all about."
"I think they're very rude statements and frankly, tell him, I will remember those statements. They're very nasty statements."
A spokesperson for Khan called Trump's views "ignorant, divisive and dangerous."
"Sadiq has spent his whole life fighting extremism, but Trump's remarks make that fight much harder for us all -- it plays straight into the extremists' hands and makes both our countries less safe," the spokesperson said in a statement.
Khan says no to I.Q. test challenge
Khan responded Monday by repeating his criticism of Trump's politics, calling it "the politics of fear at its worst," and saying Trump's remarks on Islam play "straight into the extremists' hands and makes both our countries less safe."
He rebuffed Trump's suggestion of taking an I.Q. test, saying "ignorance is not the same thing as lack of intelligence."
Khan told CNN last week he hoped that Trump would not win the U.S. election
, describing him as "somebody who is trying to divide, not just your communities in America but who is trying to divide America from the rest of the world."
Trump, who in December issued a press release "calling for a total and complete shutdown of Muslims entering the United States," appeared to modify his position last week.
He said such a ban "hasn't been called for yet" and was "only a suggestion."
Britain 'a great ally'
In the same interview, Trump said Britain wouldn't be hurt "at all" in terms of trade negotiations with the United States if it exited the European Union.
"I don't think they'll be hurt at all. I mean, they'll have to make their own deal. Britain's been a great ally," he said.
The United States is in the midst of negotiating with the European Union a trade pact called the Trans-Atlantic Trade and Investment Partnership, which is intended largely to smooth out regulatory differences.
President Barack Obama had warned in an April visit to London that Britain would move to "the back of the queue" in negotiating trade deals with the United States should it exit the European Union.
He said a trade deal between the two countries could still happen, "but it's not going to happen any time soon because our focus is in negotiating with a big bloc, the European Union, to get a trade agreement done."
Trump, despite his issues with Cameron and Khan, wouldn't criticize Britain as a country.
"Britain's such a great ally that they went into things that they shouldn't have gone into -- like, as an example, going into Iraq, OK? With me, they'll always been treated fantastically," he said.
He said he wouldn't treat Britain any differently in terms of trade negotiations were it to leave the European Union.
"I mean, I'm going to treat everybody fairly but it wouldn't make any difference to me whether they were in the EU or not," he said.
Britain, he said, would certainly not be at the "back of the queue."
UK voters will decide in a referendum June 23 whether to leave the European Union.