The memo, which was made available to all members of the House, is said to contend that officials from the two agencies were not forthcoming to a Foreign Intelligence Surveillance Court judge.
The White House has suggested that Trump wants to let the public see the memo, but his own Justice Department has argued against it.
While the panel voted to release that memo to the entire House, Republicans expressed concern that publicly releasing the minority memo would damage sensitive intelligence sources and methods, according toRep. Last week, the DOJ sent Mr. Nunes a letter urging him not to release it - stating that such an act would be "extremely reckless".
In a sign of the intensely partisan trench warfare that's broken out over the direction of Washington's multiple Russian election meddling probes, GOP committee members during the same hearing also voted down releasing an alternate memo complied by Democrats.
At the behest of Trump, White House chief of staff John Kelly and other White House officials contacted Justice Department officials in the past week to convey the president's displeasure with the department's leadership on the issue specifically, the official said.
Democrats efforts to have their own memo released were voted down by the committee, Schiff said.
Page to the House Intelligence Committee that in July 2016 he traveled to Moscow, where he gave a speech that was critical of USA policy toward Russia and met privately with Russian officials, including the country's deputy prime minister.
That's in the wake of news reports that he sought to fire the special counsel.
The committee is also expected to discuss a dueling memo drafted by the committee's top Democrat, Rep. Adam Schiff, though it's unclear if there will be an effort to make that memo public, too.
"I am heartsick, as should anyone be who cares about democracy and our nation's security", said Jeffrey Smith, a former general counsel at the Central Intelligence Agency.
President Donald Trump now has five days to object to the four-page memo's public release.
"Committee Republicans JUST voted to declassify their spin "memo" and prohibit release of the Democratic response in what they claimed was 'the interests of full transparency, '" Schiff tweeted Monday night.
Democrats on the panel have said that the Nunes memo is misleading and that the representative had not even reviewed firsthand the information on which it is based. In Republicans' construction, biased special agents within the FBI took scurrilous Democratic-funded opposition research and used it to launch a baseless investigation of the Trump camp's ties to Russian Federation.
Conway's insistence that the White House remain silent on the memo's contents, however, is in direct contrast with the majority of Republicans, who have continued to speak out about it at every given opportunity. But he insisted that Mueller's job appeared to be in no immediate danger, pointing to the political costs if Trump did remove him.