The league and Argentina, Brazil, Chile, Colombia, Costa Rica, El Salvador, Guatemala, Honduras, Mexico, Nicaragua and Peru joined the American Civil Liberties Union, the Southern Poverty Law Center and several other civil and immigrant rights groups in arguing the Georgia law is unconstitutional because it's preempted by federal law.
Their federal class-action lawsuit also asks U.S. District Judge Thomas Thrash to keep the measure from going into effect while their case is still pending.
Much of the law is set to take effect July 1.
Republican Georgia Gov. Nathan Deal and other state officials asked Thrash to dismiss the class-action suit, arguing the law is constitutional, the groups have no standing to sue and the state should be immune from such lawsuits anyway.
Trash plans his first hearing on the case Monday. He said he might rule that day on the plaintiffs' request to block the law, The Atlanta Journal-Constitution reported.
He also plans to hear arguments Monday on the state's motion to dismiss the case.
The immigration enforcement law, also known as state House Bill 87, lets police check the immigration status of suspects who can't provide accepted identification. It also lets law enforcement agencies detain and hand over to federal authorities anyone found to be in the country illegally. And it makes lying about immigration status on a job application a felony.
Starting in January it also requires many employers to use a federal database to check the immigration status of prospective employees.
Critics argue House Bill 87 is similar to Arizona's controversial Senate Bill 1070 anti-illegal immigration measure that provoked a nationwide debate and a U.S. Justice Department lawsuit last year.
Proponents of the Georgia law say the state needs to curb illegal immigration because Washington has failed to secure the nation's borders. They argue illegal immigrants burden the state's taxpayer-funded resources, including public schools, jails and hospitals.