Donald Trump said Sunday that President Obama should resign because he did not use the term “radical Islam” in remarks about the massacre at an Orlando gay nightclub.

“In his remarks today, President Obama disgracefully refused to even say the words ‘Radical Islam.’ For that reason alone, he should step down,” the presumptive Republican presidential nominee said in a statement.

Mr. Trump also said likely Democratic nominee Hillary Clinton should get out of the White House race if she can’t use those words.

“If Hillary Clinton, after this attack, still cannot say the two words ‘Radical Islam’ she should get out of this race for the Presidency,” said Mr. Trump.

Mrs. Clinton said in a tweet: “This was an act of terror … This was also an act of hate.”

Throughout the campaign, Mr. Trump has made an issue of the refusal by Mr. Obama and Mrs. Clinton to use any form of the words “Islam” or “Muslim” when talking about the terrorist threat facing America.

“If we do not get tough and smart real fast, we are not going to have a country anymore,” he said. “Because our leaders are weak, I said this was going to happen — and it is only going to get worse. I am trying to save lives and prevent the next terrorist attack. We can’t afford to be politically correct anymore.”

He called for tightening immigration laws and said Mrs. Clinton supported expanded immigration from Middle East countries.

The billionaire businessman has been the target of fierce criticism, including being labeled a “bigot” and “un-American,” for proposing a temporary ban on Muslims entering the U.S. He proposed the ban after 14 people were killed in a December terrorist attack in San Bernardino by a husband-and-wife team liked to the Islamic State.

The Orlando attack has once again thrust terrorism to the forefront of political debate.

“We need to protect all Americans, of all backgrounds and all beliefs, from Radical Islamic Terrorism — which has no place in an open and tolerant society,” said Mr. Trump in his statement. “Radical Islam advocates hate for women, gays, Jews, Christians and all Americans. I am going to be a President for all Americans, and I am going to protect and defend all Americans. We are going to make America safe again and great again for everyone.”

In brief remarks at the White House, Mr. Obama said the gunman in Orlando was “filled with hatred.”

“Although it’s still early in the investigation, we know enough to say that this was an act of terror and an act of hate,” said the president.

He did not use the phrase “radical Islam” or any similar identification.

Omar Siddiqui Mateen, a 29-year-old U.S. citizen, reportedly pledged allegiance to the Islamic State in a 911 call before he was killed in a shootout with authorities. Mr. Trump early on identified the act as radical Islamic terrorism.

“Our nation was attacked by a radical Islamic terrorist. It was the worst terrorist attack on our soil since 9/11, and the second of its kind in 6 months,” said Mr. Trump, extending “deepest sympathy” to the victims and their families.

He said that the gunman was the “son of an immigrant from Afghanistan who openly published his support for the Afghanistani Taliban and even tried to run for President of Afghanistan.”

He noted a Pew Research Center study that found 99 percent of Afghans support Shariah law, a legal system based on Islam that Mr. Trump called “oppressive.” While Muslims vary on their details of Shariah, homosexuality is always a criminal offense under it and sometimes a capital one, as in Iran and Saudi Arabia.

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