The officials’ decision to keep information from Mr. Trump underscores the deep mistrust that has developed between the intelligence community and the president over his team’s contacts with the Russian government, as well as the enmity he has shown toward U.S. spy agencies. On Wednesday, Mr. Trump accused the agencies of leaking information to undermine him.
In some of these cases of withheld information, officials have decided not to show Mr. Trump the sources and methods that the intelligence agencies use to collect information, the current and former officials said. Those sources and methods could include, for instance, the means that an agency uses to spy on a foreign government.
A White House official said: “There is nothing that leads us to believe that this is an accurate account of what is actually happening.”
A spokesman for the Office of Director of National Intelligence said: “Any suggestion that the U.S. intelligence community is withholding information and not providing the best possible intelligence to the president and his national security team is not true.”
Intelligence officials have in the past not told a president or members of Congress about the ins and outs of how they ply their trade. At times, they have decided that secrecy is essential for protecting a source, and that all a president needs to know is what that source revealed and what the intelligence community thinks is important about it.
But in these previous cases in which information was withheld, the decision wasn’t motivated by a concern about a president’s trustworthiness or discretion, the current and former officials said.
It wasn’t clear Wednesday how many times officials have held back information from Mr. Trump.
The officials emphasized that they know of no instance in which crucial information about security threats or potential plotting has been omitted. Still, the misgivings that have emerged among intelligence officials point to the fissures spreading between the White House and the U.S. spy agencies.
Mr. Trump, a Republican, asked Monday night for the resignation of Mike Flynn, his national security adviser, after the White House said the president lost trust in him, in part, because he misstated the nature of his conversations with the Russian ambassador.
On Wednesday, Mr. Trump castigated the intelligence agencies and the news media, blaming them for Mr. Flynn’s downfall.
“The real scandal here is that classified information is illegally given out by ‘intelligence’ like candy. Very un-American!” Mr. Trump tweeted.
Mr. Trump doesn’t immerse himself in intelligence information, and it isn’t clear that he has expressed a desire to know sources and methods. The intelligence agencies have been told to dramatically pare down the president’s daily intelligence briefing, both the number of topics and how much information is described under each topic, an official said. Compared with his immediate predecessors, Mr. Trump so far has chosen to rely less on the daily briefing than they did.
The current and former officials said the decision to avoid revealing sources and methods with Mr. Trump stems in large part from the president’s repeated expressions of admiration for Russian President Vladimir Putin and his call during the presidential campaign for Russia to continue hacking the emails of his Democratic rival, Hillary Clinton.
U.S. intelligence agencies have concluded that Russia stole and leaked emails from Mrs. Clinton’s campaign to undermine the election process and try to boost Mr. Trump’s chances of winning, an allegation denied by Russian officials.
Several of Mr. Trump’s current and former advisers are under investigation for the nature of their ties to Moscow, according to people familiar with the matter. After Mr. Flynn’s dismissal, lawmakers have called on the government to release the transcripts of his conversations with Russian Ambassador Sergey Kislyak and to disclose whether Mr. Trump was aware of or directed Mr. Flynn’s conversations.
Two senior intelligence officials denied Wednesday that Mr. Flynn had engaged in extensive contacts with Russian officials. One of the officials said none of the other advisers had extensive contacts with Russian officials or engaged in any pattern of contacts.
Rep. Adam Schiff (D., Calif.), the ranking member of the House Intelligence Committee, said he has heard concerns from officials about sharing especially sensitive information with Mr. Trump.
“I’ve talked with people in the intelligence community that do have concerns about the White House, about the president, and I think those concerns take a number of forms,” Mr. Schiff said, without confirming any specific incidents. “What the intelligence community considers their most sacred obligation is to protect the very best intelligence and to protect the people that are producing it.”
“I’m sure there are people in the community who feel they don’t know where he’s coming from on Russia,” Mr. Schiff said.
Tensions between the spy agencies and Mr. Trump were pronounced even before he took office, after he publicly accused the Central Intelligence Agency and others of leaking information about alleged Russian hacking operations to undermine the legitimacy of his election win. In a meandering speech in front of a revered CIA memorial the day after his inauguration, Mr. Trump boasted about the size of his inaugural crowd and accused the media of inventing a conflict between him and the agencies.
In a news conference on Wednesday with Prime Minister Benjamin Netanyahu of Israel, Mr. Trump again lashed out at the media and intelligence officials, whom he accused of “criminal” leaks about Mr. Flynn’s conversations with the Russian ambassador last December.
Mr. Trump didn’t explain Wednesday why he asked for Mr. Flynn’s resignation. Instead, he suggested the leaks and the media were to blame for his ouster.
“General Flynn is a wonderful man. I think he’s been treated very, very unfairly by the media,” Mr. Trump said. “And I think it’s really a sad thing that he was treated so badly.”
“I think in addition to that from intelligence, papers are being leaked, things are being leaked,” Mr. Trump said. “It’s criminal action. It’s a criminal act and it’s been going on for a long time before me but now it’s really going on.”
Reviving his line of criticism against intelligence officials during the transition, Mr. Trump said the “illegally leaked” information was from people with political motivations. “People are trying to cover up for a terrible loss that the Democrats had under Hillary Clinton,” Mr. Trump said.
A person close to Mr. Trump said he was reluctant to let go of Mr. Flynn because Mr. Flynn had vigorously supported him at a stage of his presidential campaign when few people did. Mr. Trump also felt Mr. Flynn did nothing wrong in his conversations with the U.S. ambassador to Russia and had good intentions.
“They both continue to support each other,” this person said.
For intelligence veterans, who had hoped that Mr. Trump’s feud with the agencies might have subsided, Wednesday’s comments renewed and deepened concerns.
“This is not about who won the election. This is about concerns about institutional integrity,” said Mark Lowenthal, a former senior intelligence official.
“It’s probably unprecedented to have this difficult a relationship between a president and the intelligence agencies,” Mr. Lowenthal said. “I can’t recall ever seeing this level of friction. And it’s just not good for the country.”
Several congressional probes are examining Russia’s alleged meddling in the election. On Wednesday, the Republican and Democratic leaders of the Senate Judiciary Committee requested a Justice Department briefing and documents related to Mr. Flynn’s resignation, including details of his communications with Russian officials.
—Damian Paletta contributed to this article.