Aereo sues to block more CBS lawsuits

But in its court filing on Monday, Aereo argued that the broadcast companies cannot seek a "do-over" in new courts.

"It is not proper for parties to attempt to re-litigate claims that are pending, let alone already decided. Among other reasons, it would be highly inefficient and a waste of judicial resources," the Web company wrote in the filing.

“These public relations and legal maneuvers do not change the fundamentally illegal nature of Aereo’s supposed business," CBS said in a statement. "The issue of unauthorized streaming of copyrighted television programming is now being contested in the 2nd Circuit and the 9th Circuit, and wherever Aereo attempts to operate there will be vigorous challenges to its illegal business model.”

Aereo uses tiny antennas to pick up free over-the-air broadcast television signals and then transmits the video to its customers over the Internet. Customers pay a monthly fee to rent access to an antenna, which allows them to record and watch network television on their mobile devices and computers.

Aereo claims that it is only helping people access free television, but the broadcasters argue the company should have to pay for the right to retransmit their signals, just like cable and satellite providers already do.