Obama, a Democrat who endorsed his former Secretary of State Hillary Clinton in the 2016 White House race, has made clear his dismay over Trump, a New York businessman who has proposed temporarily banning Muslims from entering the United States and building a wall on the U.S. border with Mexico.
On Tuesday Obama questioned why leading Republicans have not withdrawn their support for their presidential nominee. On Thursday he dismissed as ridiculous Trump's claims that the election may be rigged.
"Of course the elections will not be rigged. What does that mean?" Obama said with exasperation. "If Mr. Trump is up 10 or 15 points on Election Day and ends up losing, then maybe he can raise some questions. That doesn’t seem to be the case at the moment."
Trump is trailing Clinton in polls.
Despite his disdain, Obama said Trump would get the top secret briefings on world crises and security threats to which he, Clinton and their respective vice presidential running mates are entitled.
Some Republicans have said Clinton should be denied access to such briefings because of her handling of classified material on a private email server while she was secretary of state.
Obama on Thursday, speaking to reporters at the Pentagon, made clear that both candidates would be treated equally.
"We are going to go by the law, which is that, in both tradition and the law, that if somebody is the nominee ... they need to get a security briefing so that if they were to win, they are not starting from scratch in terms of being prepared," Obama said.
"What I will say is that they have been told these are classified briefings," he added, in response to a question about whether he was concerned about Trump obtaining the classified information. "And if they want to be president, they got to start acting like president, and that means being able to receive these briefings and not spread them around."
Trump has placed blame on Clinton and Obama for the rise of Islamic State, also known as ISIS.
"The Obama-Clinton foreign policy gave rise to ISIS, made Iran flush with cash, and is now admitting vast numbers of refugees and migrants into the United States from some of the most volatile regions in the world," Trump senior policy adviser Stephen Miller said in a statement.
"But none of this is surprising from an Administration that allowed its Secretary of State to threaten the country with a private email server, delete her records, and lie about it to us all," Miller said.
Obama, who was meeting with his national security advisers about the fight against Islamic State, also made a subtle jab at Trump for his dispute with a Muslim couple whose U.S. Army captain son died in Iraq. Obama lauded "patriotic Muslim Americans" who fight in the U.S. armed forces.