Mr. Rosendale entered the Republican primary race less than a week ago, but Donald J. Trump’s quick endorsement of his main rival left him facing an uphill fight.
The incident escalated a campaign by the ousted Law and Justice party to resist the transfer of power after it lost its parliamentary majority in October.
With the former president busy defending himself in court from 91 felony charges, his campaign has deployed high-profile conservatives to help fill the gaps in Iowa.