The Democratic governor-elect of Arizona, Katie Hobbs, asked a court on Monday to sanction her defeated Republican rival, Kari Lake, over her failed effort to overturn the election result.

In legal filings, Hobbs also pointed to a now-deleted tweet from Lake in which the Republican suggested the judge overseeing her lawsuit had acted unethically.

On Saturday, Judge Peter Thompson rejected Lake’s lawsuit challenging the counting and certification of the November election in an attempt to be declared the winner despite a lack of evidence of voter fraud.

Hobbs subsequently joined a motion by Maricopa county for sanctions against Lake and her attorneys, in which the county deputy attorney, Thomas P Liddy, said the Republican filed a “groundless” lawsuit for a “frivolous pursuit”.

“Enough really is enough,” Liddy wrote in the motion. “It is past time to end unfounded attacks on elections and unwarranted accusations against elections officials.”

The motion had “no basis in law or fact”, lawyers for Lake said on Monday evening, asking the court to deny the request.

“Trust in the election process is not furthered by punishing those who bring legitimate claims as plaintiff did here. In fact, sanctioning plaintiff would have the opposite effect.”

Sanctions would be in the form of a financial penalty imposed for violation of a court rule or for misconduct.

Lake targeted Hobbs, currently Arizona’s secretary of state but governor from next week, along with top officials in Maricopa county. The Republican’s suit claimed “hundreds of thousands of illegal ballots infected the election” in the state’s most populous county.

In a separate filing, Hobbs asked the superior court in Maricopa county to award her more than $600,000 to compensate for fees and expenses accrued in defending Lake’s lawsuit.

Lake, a former TV news anchor, was one of the most high-profile Republicans in the midterm elections to embrace Donald Trump’s lie about voter fraud in 2020. She lost but refused to concede and continued making unconfirmed claims about election improprieties.

Lake posted the later-deleted tweet on Monday morning, the Hill reported. It suggested Marc Elias, founding partner of the election law firm representing Hobbs, sent Thompson an email telling him “what to say” in his dismissal.

The tweet quoted Rachel Alexander, who made the suggestion in an opinion piece for Townhall.com.

“The dismissal of Kari Lake’s election lawsuit shows voter disenfranchisement no longer matters,” the Hill quoted the now-deleted tweet as saying. “Legal experts believe his decision [by Judge Thompson] was ghostwritten, they suspect top leftwing attorneys like Marc Elias emailed him what to say.”

Lake’s camp maintained in court papers she had “simply retweeted” Alexander, and said: “Tweets, especially those authored by others, do not support sanctions under Arizona law.”

Elias commented, tweeting: “I’ve had a lot of lies told about me today – more than usual … More than even after the 2020 election. I always first point them out and ask for them to be deleted. Honorable people do so. But, the people still lying about me are doing it on purpose. But I’m done. Goodnight.”