Minnesota Attorney General Lori Swanson says she continues to review the president's revised travel ban order and has yet to decide whether to join other states in filing a new complaint against it.
On Monday, Washington, Oregon, New York and Massachusetts are expected to file a new complaint challenging the revised travel ban. Hawaii also launched its own lawsuit.
In late January, Minnesota joined with Washington in filing an initial lawsuit that resulted in a federal judge halting its implementation.
Trump's revised ban bars new visas for people from six predominantly Muslim countries. It also temporarily shuts down the U.S. refugee program. But it does not affect current visa holders and it removes language that would give priority to religious minorities.