Coats and Rogers refused to comply with the requests, which they both deemed to be inappropriate, according to two current and two former officials, who spoke on the condition of anonymity to discuss private communications with the president.
Trump sought the assistance of Coats and Rogers after FBI Director James B. Comey told the House Intelligence Committee on March 20 that the FBI was investigating "the nature of any links between individuals associated with the Trump campaign and the Russian government and whether there was any coordination between the campaign and Russia's efforts."
Trump's conversation with Rogers was documented contemporaneously in an internal memo written by a senior NSA official, according to the officials. It is unclear if a similar memo was prepared by the Office of the Director of National Intelligence to document Trump's conversation with Coats. Officials said such memos could be made available to both the special counsel now overseeing the Russia investigation and congressional investigators, who might explore whether Trump sought to impede the FBI's work.
White House officials say Comey's testimony about the scope of the FBI investigation upset Trump, who has dismissed the FBI and congressional investigations as a "witch hunt." The president has repeatedly said there was no collusion.
Current and former senior intelligence officials viewed Trump's requests as an attempt by the president to tarnish the credibility of the agency leading the Russia investigation.
A senior intelligence official said Trump's goal was to "muddy the waters" about the scope of the FBI probe at a time when Democrats were ramping up their calls for the Justice Department to appoint a special counsel, a step announced last week.
Senior intelligence officials also saw the March requests as a threat to the independence of U.S. spy agencies, which are supposed to remain insulated from partisan issues.
"The problem wasn't so much asking them to issue statements, it was asking them to issue false statements about an ongoing investigation," a former senior intelligence official said of the request to Coats.
The NSA and Brian Hale, a spokesman for Coats, declined to comment, citing the ongoing investigation.
"The White House does not confirm or deny unsubstantiated claims based on illegal leaks from anonymous individuals," a White House spokesman said. "The president will continue to focus on his agenda that he was elected to pursue by the American people."
In addition to the requests to Coats and Rogers, senior White House officials sounded out top intelligence officials about the possibility of intervening directly with Comey to encourage the FBI to drop its probe of Michael Flynn, Trump's former national security adviser, according to people familiar with the matter. The officials said the White House appeared uncertain about its power to influence the FBI.
"Can we ask him to shut down the investigation? Are you able to assist in this matter?" one official said of the line of questioning from the White House.
Rep. Adam B. Schiff (Calif.), the ranking Democrat on the House intelligence committee, said the report is "yet another disturbing allegation that the President was interfering in the FBI probe." Schiff said in a statement that Congress "will need to bring the relevant officials back to testify on these matters, and obtain any memoranda that reflect such conversations."
The new revelations add to a growing body of evidence that Trump sought to co-opt and then undermine Comey before he fired him May 9. According to notes kept by Comey, Trump first asked for his loyalty at a dinner in January and then, at a meeting the next month, asked him to drop the probe into Flynn. Trump disputes those accounts.
Current and former officials said that Trump either lacks an understanding of the FBI's role as an independent law enforcement agency or does not care about maintaining such boundaries.
Trump's effort to use the director of national intelligence and the NSA director to dispute Comey's statement and to say there was no evidence of collusion echoes President Richard Nixon's "unsuccessful efforts to use the CIA to shut down the FBI's investigation of the Watergate break-in on national security grounds," said Jeffrey H. Smith, a former general counsel at the CIA. Smith called Trump's actions "an appalling abuse of power."
Trump made his appeal to Coats days after Comey's testimony, according to officials.
That same week, Trump telephoned Rogers to make a similar appeal.
In his call with Rogers, Trump urged the NSA director to speak out publicly if there was no evidence of collusion, according to officials briefed on the exchange.
Rogers was taken aback but tried to respectfully explain why he could not do so, the officials said. For one thing, he could not comment on an ongoing investigation. Rogers added that he would not talk about classified matters in public.
While relations between Trump and Comey were strained by the Russia probe, ties between the president and the other intelligence chiefs, including Rogers, Coats and CIA Director Mike Pompeo, appear to be less contentious, according to officials.
Rogers met with Trump in New York shortly after the election, and Trump's advisers at the time held him out as the leading candidate to be the next director of national intelligence.
The Washington Post subsequently reported that President Barack Obama's defense secretary and director of national intelligence had recommended that Rogers be removed as head of the NSA.
Ultimately, Trump decided to nominate Coats, rather than Rogers. Coats was sworn in just days before the president made his request.
In February, the Trump White House also sought to enlist senior members of the intelligence community and Congress to push back against suggestions that Trump associates were in frequent contact with Russian officials. But in that case, the White House effort was designed to refute news accounts, not the testimony of a sitting FBI director who was leading an open investigation.
Trump and his allies in Congress have similarly sought to deflect scrutiny over Russia by attempting to pit U.S. intelligence agencies against one another.
In December, Trump's congressional allies falsely claimed that the FBI did not concur with a CIA assessment that Russia intervened in the 2016 election to help Trump win the White House. Comey and then-CIA Director John Brennan later said that the bureau and the agency were in full agreement on Moscow's intentions.
As the director of national intelligence, Coats leads the vast U.S. intelligence community, which includes the FBI. But that does not mean he has full visibility into the FBI probe. Coats's predecessor in the job, James R. Clapper Jr., recently acknowledged that Comey did not brief him on the scope of the Russia investigation. Similarly, it is unclear to what extent the FBI has brought Coats up to speed on the probe's most sensitive findings.