Lisa Page defied that subpoena to appear on Wednesday before the House Judiciary and Oversight and Government Reform Committees.
House Judiciary Chairman Robert Goodlatte said Page has known for months that the panel has sought her testimony, and the committee will use "all tools at our disposal" to obtain it.
House Speaker Paul Ryan said he was willing to hold her in contempt.
"Ex-FBI LAYER Lisa Page today defied a House of Representatives issued Subpoena to testify before Congress!"
Indeed, as early as December 19, Goodlatte and oversight committee chair Trey Gowdy (R-S.C.) sent a letter to Attorney General Jeff Sessions and his deputy, Rod Rosenstein, asking the Justice Department to make Page available for an interview.
An FBI official will testify Thursday before two House committees investigating allegations of bias in the agency against President Donald Trump.
Strzok was the lead agent on both the probe of Clinton's mishandling of classified information and the counterintelligence investigation of alleged ties between the Trump campaign and Russian Federation.
House Republicans have suggested the Federal Bureau of Investigation was conspiring against Trump during and after his presidential campaign, and the two committees are investigating decisions made by the agency and the Justice Department during the election.
The president has repeatedly painted Mueller's investigation as a tainted witch-hunt led by Democrats.
Rep. Devin Nunes (R-CA) threatened Page that he would enforce the subpoena, but has yet to do so. "All she is asking is to be treated as other witnesses have under the Committees' own rules".
Page's attorney Amy Jeffress said in a statement to CNN that she has been working with the committee staff to arrange for her client's "voluntary appearance". Bob Goodlatte, said Wednesday that Republicans recently were forced to call in U.S. Marshals to serve former Federal Bureau of Investigation lawyer Lisa Page with a subpoena to testify before Congress, as he accused Page of "apparently" having "something to hide". Jeffress said they are also still waiting on documents from the Federal Bureau of Investigation to prepare.
The two committees' "bullying tactics here are unnecessary", she added. "We expect them to agree to another date so that Lisa can appear before the Committees in the near future".
Page was subpoenaed to provide a deposition behind closed doors on Wednesday, but she didn't appear under Jeffress's advice.
The Judiciary and Oversight panels have already spent much of the summer holding hearings and interviews critical of the Federal Bureau of Investigation and Justice Department.
Strzok will testify publicly before the committees on Thursday. Both were removed from the Mueller probe past year after the Justice Department's internal watchdog made the special counsel aware of the anti-Trump text messages.
Jeffress said in her Wednesday statement that Page has already offered 36 hours of testimony to the Justice Department's inspector general's office.