Jeffress accused the panels of using unnecessary "bullying tactics" to push Page into an interview immediately, especially when "she has offered to voluntarily appear before the committees later this month".
Strzok was removed from Mueller's team when the texts were discovered past year. "All she is asking is to be treated as other witnesses have under the committees' own rules", Jeffress said.
"It appears Lisa Page has something to hide", said House Judiciary Committee Chairman Bob Goodlatte (R-VA.) on Tuesday.
He added: 'If she wants to come plead the Fifth, that's her choice.
"Despite repeated promises by Republicans that they would not interfere with the ongoing criminal investigation being conducted by Special Counsel Robert Mueller, they asked hundreds of questions during our recent interview of Peter Strzok demonstrating that their investigation has become exactly that - an attempt to obstruct Special Counsel Mueller's work and act as President Trump's defense counsel", Mr. Cummings said.
Lisa Page has ignored a subpoena from Congressional investigators who have abandoned the Russian Federation investigation and pivoted to investigating the FBI instead. Page, who exchanged anti-Trump text messages with FBI official Peter Strzrok during the Clinton email investigation, was asked to appear for an interview with the committees.
Jerry Nadler, the top Democrat on the Judiciary Committee, said the threat of holding Page in contempt was a "charade", arguing there was no reason why she couldn't review the documents and come in for an interview next week.
The president has repeatedly painted Mueller's investigation as a tainted witch-hunt led by Democrats.
The committee had scheduled Page's closed-door testimony one day before Strzok is set to testify publicly before the Judiciary and Oversight committees.
In tweets, Trump has branded the couple the "FBI lovers" and said their bias was at the heart of Mueller's "Witch Hunt".
House Republicans sent a letter to Jeffress on Wednesday that gave Page three options: show up to Thursday's public hearing, attend a closed-door deposition on Friday or face contempt of Congress proceedings beginning Friday morning. Trump tweeted. "Read his hate filled and totally biased Emails and the answer is clear!" "This is an example of a congressional committee trying to find a "gotcha moment" instead of legitimately investigating Justice Department policies and practices".
While Strzok was faulted for his political bias in an inspector general report on the Clinton investigation, his attorney has argued that the inspector general also found that the investigative decisions in that probe were unaffected.
Strzok was questioned for 11 hours over his role and alleged bias in a closed hearing of the two committees two weeks ago.
The Judiciary Committee also held a contentious hearing June 28 with FBI Director Christopher Wray and Deputy Attorney General Rod Rosenstein.