The leak of transcripts of telephonic conversations between US President Donald Trump and the leaders of Mexico and Australia is a national security matter, the White House has said.

It was referring to the yesterday's incident of a leading American daily posting highly classified transcripts of Trump's conversations with Mexican President Enrique Pena Nieto and Australian Prime Minister Malcolm Turnbull.

"It's a national security matter when phone call transcripts are being leaked out. It prevents the president from being able to do what he does best, and negotiate with foreign leaders," White House Deputy Press Secretary Lindsay Walters told reporters yesterday abroad Air Force One travelling with Trump to West Virginia.

The White House officials, however, refused to comment on the specific leaks of the conversation, which was posted by The Washington Post on its website.

"What I can tell you regarding the border wall is that the president spoke about this on the campaign, continues to echo it now, and having a secure border is … something that he had promised his supporters and has continued to focus on making sure that we have a secure border," she said.

The leaks of the presidential conversation has been condemned by even Trump's critics.

"This is beyond the pale and will have a chilling effect going forward on the ability of the commander-in-chief to have candid discussions with his counterparts," Ned Price, a former National Security Council official under President Barack Obama, told The Hill.

"Granted, the White House contributed to this atmosphere by welcoming the free-for-all environment, where anonymous leaks are commonplace. But we must draw the line somewhere," Price was quoted as saying.

"I would've lost my mind if transcripts of Obama's calls to foreign leaders leaked. He wouldn't have sounded so dumb, but it's still absurd," said Tommy Vietor, another former spokesman of the National Security Council under the Obama Administration.

David Frum, a speech writer to the former US President George W Bush said that the president's opponents do a "lasting damage" to American security when they violate norms to undermine him.

"Leaking the transcript of a presidential call to a foreign leader is unprecedented, shocking, and dangerous. It is vitally important that a president be able to speak confidentially, and perhaps even more important that foreign leaders understand that they can reply in confidence," he wrote in The Atlantic magazine.

Frum said that the leak will reverberate around the world.

"No leader will again speak candidly on the phone to Washington, DC – at least for the duration of this presidency, and perhaps for longer," he said.

US Attorney General Jeff Sessions along with his top intelligence officials are scheduled to have a press conference on leaks today. The presser was however scheduled before The Washington Post released the transcripts of the presidential conversation.

Democratic Senator Mark Warner, who is Vice Chairman of the Senate Select Committee on Intelligence, expressed apprehensions that the leak may be "reflective of a chaotic White House" and demanded that the president should investigate the leaks.

"While the leak may be reflective of a chaotic White House, it still constituted a massive breach of norms and was serious enough to merit a congressional inquiry. Whether that is Intel or Judicial (committees) looking into it, somebody ought to," Warner told The Daily Beast in an interview.