Page later left the Federal Bureau of Investigation but Strzok remains.
Two congressional sources said a committee vote to hold Page in contempt could be held on Friday, which would set the stage for a full House vote next week.
"It appears that Lisa Page has something to hide", Goodlatte said. Trump tweeted. "Together with her lover, FBI Agent Peter Strzok, she worked on the Rigged Witch Hunt, perhaps the most tainted and corrupt case EVER!"
"As an additional, and final, accommodation, the [Judiciary] Committee will stay the contempt proceedings provided Lisa Page voluntarily appears on July 12, 2018, at 10:00 a.m., at a previously scheduled public hearing regarding relevant issues under investigation", Oversight Chair Trey Gowdy (R-SC) and Judiciary Chair Bob Goodlatte (R-VA) wrote.
After the Clinton probe ended and Trump won the election, both Strzok and Page joined, for a short time, the investigation led by Special Counsel Robert Mueller into possible collusion and obstruction by the Trump campaign.
"She was a part of the mess that we have uncovered over at DOJ".
Lawmakers want to question Page about her anti-Trump texts with Federal Bureau of Investigation agent Peter Strzok, with whom she was having an affair.
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.
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The [House Judiciary and Oversight] Committees' bullying tactics here are unnecessary.
Republican lawmakers have seized on a text in which Mr. Strzok discusses "an insurance policy" against the president and another in which he vowed to stop Mr. Trump from becoming president as evidence the Mueller investigation is biased.
Page's decision not to show up for the deposition Wednesday, under advice of her lawyer, prompted warnings from Goodlatte and other Republicans that the House would resort to whatever tools required to obtain her testimony, potentially including a contempt of Congress action.
Meanwhile, other GOP lawmakers slammed Page's over her refusal to appear for the interview on Wednesday, with Ron DeSantis of Florida calling it "pathetic" and Jim Jordan of OH said she was "once again showing the double standard".
"Americans across the country are alarmed at the bias exhibited by top officials at the Justice Department and Federal Bureau of Investigation, and it is imperative Congress conduct vigorous oversight to ensure that never happens again".
Trump continued his criticism of Page and Strzok on Twitter Wednesday from Europe, where he had attended a North Atlantic Treaty Organisation summit.
The Judiciary Committee also held a contentious hearing June 28 with FBI Director Christopher Wray and Deputy Attorney General Rod Rosenstein. "Total disgrace!" the president tweeted Monday.
Strzok was interviewed behind closed doors by the committees for 11 hours last month.