The 11th U.S. Circuit of Appeals issued orders denying motions filed last week by the attorneys general of the two states.
"We look forward to the oral argument and the future decision by the Court," said Lauren Kane, spokeswoman for Georgia Attorney General Sam Olens.
Alabama Attorney General Luther Strange had no immediate comment on the court order Thursday, his office said.
Both Olens and Strange had said last week that the Supreme Court's ruling in Arizona would be relevant to the consideration of the appeals in their cases.
The Supreme Court said Dec. 12 that it would review a federal appeals court ruling that blocked parts of the Arizona law. One part requires that police, while enforcing other laws, question a person's immigration status if officers suspect he or she is in the country illegally.
The Obama administration challenged the Arizona law, arguing that regulating immigration is the job of the federal government, not states. The Department of Justice also challenged similar laws in Alabama, South Carolina and Utah. Civil liberties and immigrant rights groups also sued over measures in those states, as well as in Georgia and Indiana.
Karen Tumlin, a lawyer for the National Immigration Law Center, which is arguing the cases in both Alabama and Georgia, said she was pleased.
"We're happy that those cases will move forward," she said.
The groups challenging the laws had not opposed Georgia's request for delayed action, because they were satisfied with the lower court's ruling temporarily blocking parts of the law.
But the groups had filed a motion opposing Alabama's request for a stay. Parts of that state's law challenged by the group have already taken effect after a federal judge declined to block them.
Associated Press writers Greg Bluestein in Atlanta and Bob Johnson in Montgomery, Ala., contributed to this report.