Sen. Charles Schneider, R-West Des Moines, filled in for Dix at the start of Monday's session and the majority leader did not make any public comments during the day's proceedings.
Sen. Dix made headlines earlier this year after the state settled a lawsuit with former Iowa Senate GOP staffer Kirsten Anderson, who claimed she was sacked after complaining about sexual harassment in Senate Republican offices. Sen.
Republican State Senator Amy Sinclair recently introduced a bill that would require Iowa's public colleges and universities to formally recognize and respect the right of student organizations to impose religious requirements for leadership positions, as well as banning so-called "free speech zones".
"I believe he made the right decision for himself and for his district, but most importantly, I believe he made the decision in the best interest of his family", Whitver said in his statement.
"Iowans hold their elected officials to a high standard; they expect us to lead", said Reynolds.
This is a reelection year for Dix, who serves Iowa's 25th Senate district, which includes all of Hardin County, all of Grundy County and portions of Story and Butler Counties.
Iowa Senate President Jack Whitver (R-Ankeny) told the newspaper that he was unaware of any relationship between Dix and the lobbyist, and he declined to comment on the video. It claims Sen. Dix is kissing a lobbyist for a municipality group.
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Legislative leaders in the Republican-controlled Iowa House have not commented on Dix, who had been a top Republican in the Senate for several years.
"With what little I know, I'm certainly disappointed in what I'm hearing", said Reynolds. "I expect to lead".
Dix has been under pressure in the past year for his role in the sacking of Kristen Anderson, a communications director who complained about lewd behaviour in the Republican Senate caucus office.
That website said the video came from an anonymous person who saw the two in a bar and recognized Sen. Dix.
A married Republican senate leader has stepped down after video emerged showing him making out with a woman in a bar. The ex-employee filed a lawsuit several years ago claiming she was sacked after reporting misconduct in the workplace that included the use of sexual language.
Dix appointed former Ambassador Mary Kramer to consult on steps that needed to take place in the Iowa Senate, and later released an internal review that found that sexual harassment prevention training is inadequate.
Kim Reynolds was asked about the video in her Monday press conference.