The owners of four southern Maine restaurants filed a lawsuit against Gov. Janet Mills on Monday, arguing that her plan for reopening businesses is unfair to those in three counties with stricter limits still in place.

Mills’ plan allowed businesses in rural counties to reopen last month, but businesses in York, Cumberland and Androscoggin counties, where there have been more cases of COVID-19, must wait until infection statistics show that the pandemic has eased. Specifically, her order bans restaurants in those three counties from offering dine-in services until a date to be determined later, while restaurants in the 13 more-rural counties have been offering dine-in eating for nearly a month.

The lawsuit, filed in York County Superior Court, said that Mills overstepped her authority in adopting a restarting plan that treats counties differently. It also points out that some of the plaintiffs’ restaurants in Cumberland County are just a few miles from the border with Oxford County, where restaurants have been permitted to reopen. One of the restaurants is just 10 miles from its closest competitor in Oxford County.

The restaurants are the Morning Glory Diner in Bridgton, the Campfire Grille in Bridgton, the Olde Mill Tavern in Harrison and the Shed Restaurant and Willy’s Market in Acton.

Ray Richardson, a conservative talk show host on WLOB radio, on Monday called Mills’ plan “draconian.” Richardson led the drive for the lawsuit and said supporters hired a law firm based in Indianapolis to make sure it would be beyond any potential influence from Mills, a lawyer and former state attorney general.

“We didn’t want any law firm in Maine to feel pressure from the governor,” Richardson said.

The suit asks for a preliminary injunction and an emergency hearing on the suit.

It will be up to a judge to decide whether to consider those requests, but Richardson said the suit will go forward even if the process extends beyond the date when restaurants in the three counties can reopen. He said future governors should not have unchecked power to shut down businesses after determining an emergency exists.

A lawsuit challenging Mills’ requirement that out-of-state visitors undergo a 14-day quarantine when they arrive in Maine was filed in federal court in mid-May. The federal Justice Department joined in that lawsuit, but a federal judge denied a request for preliminary injunction on May 29.

That denial has since been appealed to a federal appeals court in Boston and Mills announced Monday that beginning July 1, out-of-state visitors will not have to comply with the quarantine if they have tested negative for COVID-19 within 72 hours of arriving in Maine. Visitors from Vermont and New Hampshire will be completely exempt.

Richardson said he and two groups that back him are talking with lawmakers about amending the state constitution to bar governors from declaring an emergency for more than 14 days. Longer emergencies would require backing from the Legislature, he said.

A constitutional amendment would require an act of the Legislature and approval by voters in a referendum.