T-Mobile US Inc. and Sprint Corp. , whose union was blessed by the Justice Department last week, are still wrangling with a group of state attorneys general trying to sink the wireless companies’ merger in court. But the very conditions the federal government imposed on the deal could make the states’ effort even more challenging.

Concerns about an antitrust suit brought by a group of states weighed Monday on shares of the wireless companies and Dish Network Corp. , which is in line to get assets being sold off in a deal reached with the Justice Department.

The states, led by New York and California, filed suit to block the deal on June 11, before the Justice Department had made up its mind on the $26 billion-plus transaction. The department gave the green light Friday, after the companies agreed to a host of asset sales and conditions, including ones designed to set up satellite-TV provider Dish Network Corp. as a new competitor in the wireless sector.

T-Mobile and Sprint also have the backing of the Federal Communications Commission, which signaled its approval after the companies agreed to sell Sprint’s Boost Mobile brand, expand wireless broadband access and refrain from raising prices for three years.

Now, the 13 states and the District of Columbia likely will have to litigate against the deal as modified to address the federal government’s competition concerns, which could make their case more complicated.