Controversy erupted in May after Muižnieks was elected as rector of the university in a tight contest with Gundars Bērziņš. Neither of the two found majority support from the university's 286-seat assembly, but Muižnieks scored more votes.
While the university's election committee said neither of the two was elected, the chairman of the assembly confirmed Muižnieks has won the vote.
The State Education Quality Service now says it has found a total of ten violations of protocol in the way Muižnieks was elected, for example the university's Constitutional Assembly did not vote on adopting the result.
The assembly convened again in June and confirmed Muižnieks, who has been rector since 2015, with majority support.
Now Šuplinska says that she well ask government ministers to familiarize themselves with the findings of the State Education Quality Service and then decide whether Muižnieks should still be appointed as rector.
In 2014 the University of Latvia had about 14,000 students. In addition to being a substantial exporter of services, the 1919-established university also owns large properties, with the university's new student campus to be finished in Rīga's Torņakalns neighborhood by 2023.