The co-host of The View was angered by Trump's criticism of her father, tweeting, "It kills you that no one will ever love you."
Strzok was fired from the bureau after text messages from 2016 were released that revealed anti-Trump remarks between himself and FBI lawyer Lisa Page.
In her first television interview since reappearing in public life, former FBI lawyer Lisa Page said that after President Trump "did that vile sort of simulated sex act" at a Minneapolis rally, "being quiet isn't making this go away."
The former FBI lawyer, who was accused by the president of being part of a "deep state" conspiracy against him, reacted to the inspector general report that exonerated her from any wrongdoing.
Trump publicly ridiculed Page's text messages with her lover, FBI agent Peter Strzok, which the president said showed bias against him.
The lawsuit filed on Tuesday in the District of Columbia comes after Donald Trump spent much of his early presidency lambasting Strzok "and his lover, the lovely Lisa Page."
President Trump said Obama "had to know" about the FBI "setup" to investigate his campaign and implied the former president may have helped initiate the Russia investigation.
Kellyanne Conway ridiculed former FBI Director James Comey as a "liar and a leaker" once again on Fox News on Wednesday.
Republican Rep. Duncan S. Hunter (CA) defended embattled Navy SEAL Chief Eddie Gallagher, who has been charged with several war crimes, at a border event in Ramona, California, on Saturday.
Strzok's "personal views never once influenced his professional actions," the fundraising campaign says.
Strzok sent anti-Trump texts to former FBI lawyer Lisa Page, with whom he was having an extra-marital affair.
Trump's lawyer appeared on Hannity.
The letter, 11 days before the election, has been widely cited as one of the potential reasons Clinton ultimately lost to Trump.
Senators Grassley and Johnson asked the Justice Department inspector general for information about text messages exchanged by a pair of senior FBI employees.
Peter Strzok sent text messages to his lover that showed his negative views about the president.