Chief Justice of the United States John Roberts Jr. told attorneys for both sides of the case to continue presenting their cases after the argument was scheduled to close Wednesday, The Washington Post reported.

The case stems from the case of Jose Ernesto Medellin, a Mexican national who confessed to participating in the rape and killing of two teenage girls in Texas in 1993. Medellin waived his Miranda rights, but wasn't informed of his right to meet with the Mexican consulate, a right guaranteed by the Vienna Convention to people arrested outside of their home countries.

He invoked that right at a death penalty appeal hearing and the Mexican government went to the International Court of Justice, which ruled that the death sentences of 51 Mexican nationals in the United States receive "review and reconsideration."

U.S. President George Bush issued a memorandum in 2005 ordering U.S. courts to abide by the decision but the Texas Court of Criminal Appeals ruled that Bush overstepped his authority in issuing the order.

It has now fallen to the Supreme Court to decide whether the International Court ruling will be upheld and whether the state of Texas acted properly in disregarding the president's memorandum.