The US government sued Arizona governor Doug Ducey and the state on Wednesday over the placement of shipping containers as a barrier on the border with Mexico, saying it is trespassing on federal lands.

The complaint filed in the US district court comes three weeks before the Republican governor steps aside for Democratic governor-elect Katie Hobbs, who has said she opposes the construction.

The complaint by the US justice department asks the court that Arizona be ordered to halt placement and remove the containers in remote San Rafael valley in easternmost Cochise county. The work placing up to 3,000 containers at a cost of $95m (£76m) is about a third complete, but protesters concerned about its impact on the environment have held up work in recent days.

“Officials from Reclamation and the Forest Service have notified Arizona that it is trespassing on federal lands,” the complaint reads. The action also seeks damages to compensate the US to fix any damage along the border.

The justice department sued on behalf of the Bureau of Reclamation, the Department of Agriculture and the Forest Service it oversees.

The US agriculture secretary, Tom Vilsack, said in a statement from Washington that the project “is not an effective barrier, it poses safety hazards to both the public and those working in the area and has significantly damaged public land”.

“We need serious solutions at our border, with input from local leaders and communities. Stacking shipping containers is not a productive solution,” Vilsack said.

Ducey told US officials earlier this week that Arizona stands ready to help remove the containers, which he says were placed as a temporary barrier. But he wants the US government to say when it will fill any remaining gaps in the permanent border wall as it announced it would a year ago.

The US “owes it to Arizonans and all Americans to release a timeline”, he wrote in a letter on Tuesday, responding to news of the pending federal complaint.

Border security was a focus of Donald Trump’s presidency and remains a key issue for Republican politicians.

The complaint was applauded by US representative Raúl Grijalva, a Democrat who represents southern Arizona. He called the project an “illegal junkyard border wall”.

Russ McSpadden, south-west conservation advocate for the Center for Biological Diversity, said the federal complaint “should be the beginning of the end of Doug Ducey’s lawless assault on protected national forestlands and endangered wildlife”.

The Associated Press contributed reporting