A frustrated President Trump said Thursday he’s ordered a Justice Department probe of leaks of classified information, and he defended fired National Security Adviser Michael Flynn, saying he “did nothing wrong” by talking to a Russian diplomat before the inauguration.

“We are looking into that very seriously,” Mr. Trump said of leaks by U.S. intelligence agencies. “It’s a criminal act. We’ve got to stop it.”

Pressed repeatedly by reporters in a 75-minute news conference on whether any of his aides had been in contact with Russia during the campaign — the subject of another leak this week — the president replied, “None that I know of.”

“Russia is a ruse. I have nothing to do with Russia. Haven’t made a phone call to Russia in years,” Mr. Trump said.

The president has been beating back accusations since the campaign that Russian operatives aided his candidacy by hacking the emails of Democratic officials to undermine rival Hillary Clinton.

Since his victory, Mr. Trump has been confronted with a steady stream of government leaks, including accounts of his phone conversations with world leaders and a dossier purportedly compiled by the Russians, in an apparent effort to undermine his presidency.

In Congress the chairmen of the House oversight and judiciary committees formally requested an investigation from the Justice Department’s inspector general to see if any officials mishandled classified information in the wake of recent intelligence-related leaks.

Mr. Trump said Thursday he believes the leaks are coming from “people probably from the Obama administration” who are holdovers in the new administration.

While complaining that Senate Democrats are still stalling on his nominee for director of national intelligence, Dan Coats, Mr. Trump expressed hope that newly appointed CIA Director Mike Pompeo and Attorney General Jeff Sessions will help stop the leaking of sensitive information.

“I think you’ll see it stopping, because now we have our people in,” the president said.

Mr. Trump downplayed reports that he plans to hire Wall Street financier Steven Feinberg to conduct a review of U.S. intelligence agencies, saying Mr. Coats, Mr. Pompeo and FBI Director James B. Comey should be able to tighten the flow of classified information.

“I hope that we’ll be able to straighten that out without using anybody else,” Mr. Trump said. “He’s offered his services and, you know, it’s something we may take advantage of. But I don’t think we’ll need that at all. I think that we are going be able to straighten it out very easily on its own.”

Stephen Hess, an analyst at the Brookings Institution who has worked for four presidents dating back to Dwight Eisenhower, said he’s never seen such an “avalanche” of leaks as in the first month of Mr. Trump’s presidency.

He called it “almost a war between the permanent government and the president.”

“We are in for quite a storm coming out of Washington,” Mr. Hess said in a podcast. “We don’t know where it’s going. We’re apt to be in for a very, very rough and serious period in the next two months, particularly as we see whether the Congress, the Republicans in the House, can continue to fall in behind the president.”

The president accused the liberal media of being co-opted by intelligence operatives who are sympathetic to Mrs. Clinton and leaking classified information to make him look bad. He said the resulting stories are a “fabricated deal to try and make up for the loss of the Democrats, and the press plays right into it.”

The accusations over Russia came to a head Monday night when Mr. Trump demanded the resignation of Mr. Flynn, the man he was counting on to carry out tougher policies against Iran and Islamist terrorists.

Mr. Flynn, a retired general, had phone conversations with the Russian ambassador to the U.S. before the inauguration, allegedly discussing Obama administration sanctions on Moscow, in a possible violation of federal law.

But the president said Mr. Flynn “was just doing his job,” and that he was fired instead for not divulging the full contents of his conversations to Vice President Mike Pence and other administration officials. Mr. Pence learned from a news story containing leaked classified information that Mr. Flynn may have discussed sanctions with the Russians, despite the vice president having publicly stated, based on conversations with Mr. Flynn, that this wasn’t the case.

“The thing is, he didn’t tell our vice president properly,” Mr. Trump said. “Then he said he didn’t remember. Either way, it wasn’t very satisfactory to me. He didn’t tell the vice president of the United States the facts, and then he didn’t remember. That wasn’t acceptable to me.”

He said Mr. Flynn is “a fine person.”

Asked if he had told Mr. Flynn to speak to the Russian ambassador, Mr. Trump replied, “I didn’t direct him, but I would have directed him if he didn’t do it. That’s his job.”

The president expressed frustration at length about the prevalent leaks of classified information since he took office.

He cited the example of details leaking about his phone call with Mexican President Enrique Pena Nieto, including Mr. Trump’s offer to send U.S. troops there to counter drug cartels.

“I called Mexico. It was a very confidential, classified call,” Mr. Trump said. “All of a sudden it’s out there for the world to see. It’s supposed to be secret. Same thing with Australia. All of a sudden people are finding out exactly what took place. The same thing took place with respect to Gen. Flynn. How does the press get this information? You know why — because it’s an illegal process.”

Critics have accused the president of hypocrisy because Mr. Trump expressed happiness several times about WikiLeaks’ publication of emails from Mrs. Clinton’s campaign chairman, John Podesta. He said the difference between those hacked emails and the government leaks is that the latter involved classified information.

“You’re talking about John Podesta saying bad things about the boss,” Mr. Trump said. “If John Podesta said that about me and he was working for me, I would have fired him so fast your head would have spun. He said terrible things about her. But it wasn’t classified information.”

The president ridiculed Mrs. Clinton’s clumsy efforts as secretary of state to “reset” U.S. relations with Russia, and said Moscow’s cooperation with Washington would benefit not only the U.S. but the entire world.

“We’re a very powerful nuclear country, and so are they,” he said. “If we have a good relationship with Russia, believe me, that’s a good thing, not a bad thing.”

Asked if he planned to respond to Russia’s deployment of a spy vessel off the East Coast of the U.S., its test-firing of a ballistic missile or the buzzing of a U.S. Navy ship with war planes, Mr. Trump said he won’t discuss possible military moves.

“I don’t have to tell you,” the president told a reporter. “I don’t have to tell you what I’m going to do in North Korea. And I don’t have to tell you what I’m going to do with Iran. You know why? Because they shouldn’t know. And eventually, you guys are going to get tired of asking that question.”

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