(CNN) Two Republican House chairmen are calling for the Justice Department to appoint a new special counsel to investigate possible Obama administration abuses of surveillance law, ratcheting up the pressure on Attorney General Jeff Sessions coming from congressional Republicans and President Donald Trump.

House Judiciary Chairman Bob Goodlatte of Virginia and House Oversight Chairman Trey Gowdy of South Carolina sent a letter to Sessions and Deputy Attorney General Rod Rosenstein on Tuesday urging them to appoint a special counsel to investigate actions by the FBI and Justice Department tied to the October 2016 Foreign Intelligence Surveillance Act warrant obtained on former Trump campaign foreign policy adviser Carter Page.

The FISA warrant was the subject of the memo from House Intelligence Chairman Devin Nunes that accused the FBI and Justice Department of relying on an opposition research dossier on Trump and Russia without telling the FISA court of the dossier's connections to Democrats.

Goodlatte and Gowdy told reporters a new special counsel was needed because crimes may have been committed and the scope was too broad for the Justice Department inspector general.

"I counted off the top of my head 24 witnesses that would be outside the reach of the inspector general," Gowdy said, specifically naming Clinton confidantes Sidney Blumenthal and Cody Shearer, who are both under scrutiny from Republicans over Shearer's notes on Trump and Russia that dossier author Christopher Steele gave to the FBI.

Gowdy also argued that a special counsel was a better venue than Congress to investigate the matter because a special counsel has more tools -- and public confidence. Gowdy has played a key role in the House Intelligence Committee's investigation into the dossier as one of the few lawmakers given access to the underlying FISA application that remains classified.

"We leak like the Gossip Girls," Gowdy said of Congress. "We don't have the ability to empanel a grand jury we don't have the ability to offer immunity; we should not be offering immunity. Executive Branch investigations are more publicly confidence-inspiring than current congressional investigations."

The FBI and Democrats have disputed the Republican allegations that the FISA process was abused. FBI Director Christopher Wray put out a rare statement accusing the Republican memo of omitting key facts, and Democrats offered up their own counter-memo that argued the FBI acted properly and the Page warrant was justified.

But those arguments have not swayed Republicans. Gowdy listed several possible areas he thought could involve criminality, including bias, misrepresenting information to the court and the manner by which information was secured.

The top Democrats on the Judiciary and Oversight Committees, Reps. Jerry Nadler of New York and Elijah Cummings of Maryland, slammed the Republican call for another special counsel Tuesday.

"The Department's Inspector General is fully capable of conducting an independent review. Here in Congress, our attention should be on investigating how Russia attacked our electoral process—not trying to protect President Trump," Cummings said in a statement.

But the letter from Goodlatte and Gowdy will escalate the pressure on Sessions to appoint a second special counsel alongside Robert Mueller, who is tasked with investigating the 2016 election and Russia -- and has taken a wide mandate to his probe that's led to numerous charges against senior officials in the Trump orbit.

Trump and some congressional Republican have criticized Mueller's probe as well as Sessions' decision to recuse himself in the matter, with several calling on Sessions to step aside at the same time that they've pushed for a second special counsel.

Trump in particular has needled is own attorney general on Twitter -- and he lambasted Sessions' decision last week to tap the inspector general to investigate.

"Why is A.G. Jeff Sessions asking the Inspector General to investigate potentially massive FISA abuse. Will take forever, has no prosecutorial power and already late with reports on Comey etc," Trump tweeted. "Isn't the I.G. an Obama guy? Why not use Justice Department lawyers? DISGRACEFUL!"

Sessions pushed back against Trump with a statement, saying the Justice Department "initiated the appropriate process that will ensure complaints against this department will be fully and fairly acted upon if necessary."

This isn't the first time Republicans have called for another special counsel. Goodlatte and other Judiciary Committee Republicans called for one to investigate the FBI and Justice Department handling of the Clinton email investigation, and GOP lawmakers also said a special counsel should investigate a uranium deal involving Russia. Gowdy, however, hadn't joined the calls for another special counsel until now.

Thus far, Sessions and Rosenstein, who appointed Mueller, have not moved to name a second special counsel. Sessions said in November he would consider appointing a special counsel to look into allegations against the Clinton Foundation.

Goodlatte and Gowdy said they had not discussed the issue with Sessions or Rosenstein before sending their letter Tuesday.