WASHINGTON — In a biting critique of the presumptive Republican nominee, President Obama said Friday that Donald J. Trump should be subjected to serious scrutiny and not be allowed to treat the presidential campaign like “a reality show.”

“We are in serious times, and this is a really serious job,” Mr. Obama said after being asked about Mr. Trump at a White House news conference. “This is not entertainment. This is not a reality show. This is a contest for the presidency of the United States.”

The president suggested that Mr. Trump’s statements and proposals would wither under “exacting standards and genuine scrutiny,” saying that particular attention must be paid to campaign promises made by Mr. Trump — or any other candidate — on issues like the budget, the economy and foreign policy.

“You know, if they take a position on international issues that could threaten war or has the potential of upending our critical relationships with other countries or would potentially break the financial system, that needs to be reported on,” Mr. Obama said.