House and Senate Republicans are following President Trump's lead by demanding investigations into the damaging leaks that have been pouring out of the federal government since President Trump took office.

Leaks that exposed former national security adviser Mike Flynn's phone call to the Russian ambassador in December, as well as conversations between Trump and foreign leaders, have frustrated Trump in his first few weeks in office. When Democrats pounced and said further investigations into the White House are warranted, Trump said the "real" issue is the leaks themselves.

"The real story here is why there are so many illegal leaks coming out of Washington," Trump tweeted.

Republicans in Congress made it clear they are ready to oblige. House Intelligence Committee Chairman Devin Nunes, R-Calif., is drafting a letter to the FBI that will ask the bureau investigate the leaks.

That includes an examination of who obtained and leaked a private telephone conversation between Flynn and Russian Ambassador Sergey Kislyak that led to Flynn's ousting late Monday.

"The chairman is drafting a letter to [FBI director James Comey] asking the FBI to look into, and report to the House Intelligence Committee on, the long series of purported leaks of classified information we've seen for the last several months," a GOP aide said.

The Senate Intelligence Committee may also look into the leaks as part of its probe into Flynn's conversations with the Russians and whether a special Foreign Intelligence Surveillance court permitted them to record that conversation, said Sen. Roy Blunt, R-Mo.

"I think there are a number of unanswered questions that need to be answered about the documents, about whether there was a FISA order," said Blunt, a member of the Senate leadership and the intelligence panel. "There are lots of things that I assure you that Intelligence Committee members will be looking at and I think we'll be talking about that even later today and later this week."

The calls involving Flynn took place during the presidential transition period, before Trump took office, and their contents were revealed in media reports by anonymous former and current U.S. officials.

"I expect for the FBI to tell me what's going on and hopefully they have a good answer," Nunes said Tuesday in response to those press accounts.

Nunes said recording and transcribing calls by Flynn "would be totally unprecedented," because Flynn is an American.

"The big problem I see here is you have an American citizen who has had his phone call recorded and leaked," Nunes said.

Nunes said strict rules govern the monitoring of American calls to foreigners and that "very few people" in government would have knowledge of the contents of such calls. The details of those calls are normally "expunged" because an American was on one end of the call and further listening would require approval from the secret Foreign Intelligence Surveillance Court.

"So somebody had to decided to keep recording those calls and then to unmask that and then leak it to the press," he said. "We don't even know who recorded this."

The Flynn leak is just one that has frustrated Republicans, and appears to be part of a string of leaks that came from information Obama administration officials accessed during the presidential transition, or leftover Obama officials who remain in the new administration but want to undermine the Trump presidency.

For example, unflattering transcripts of Trump's calls with the leaders of Mexico and Australia were leaked to the press.

The Mexico transcript highlighted Trump referring to Mexican drug cartels as "bad hombres," and telling President Enrique Pena Nieto he might sent U.S. troops to the border to "take care of it."

A leaked transcript of his call with Australian Prime Minister Malcolm Turnbull depicted Trump's disdain with an Obama agreement to take in 1,250 refugees housed in an Australian detention center.

The leaked information appeared aimed at embarrassing Trump and called into question his ability to establish relationships with important foreign allies. Republicans said they fear it will undermine Trump's presidency.

"I'm highly concerned about it," Senate Homeland Security Committee Chairman Ron Johnson, R-Wis., told the Washington Examiner. "The administration has to have the loyalty of its agencies and it's departments and it looks like this one doesn't have it."

Johnson said he wants to know who leaked Flynn's phone conversations.

"I certainly want to know what's happening here," Johnson said. "I believe there is information out in the public domain that never should have been out in the public domain.

The Flynn leak has so far been the most damaging one so far, as it led to press coverage that appears to have played a major role in his firing. Rep. Pete King, R-N.Y., a top GOP lawmaker on the Homeland Security Committee, said whoever leaked the information about the Flynn calls may have broken the law.

"If you've got those kinds of people in your midst when you are trying to conduct a top-secret operation and you've got people leaking out to the press for politically motivated purposes, that's a much greater danger than anything I hear the Democrats charging," King said. "Let's find out where the leaks are. They need to be rooted out."