Medellin's execution was the fifth this year in Texas
A Mexican man whose case drew international attention has been executed in Texas for the rape and murder of a 16-year-old girl in 1993.
Jose Medellin, 33, was put to death by lethal injection after the US Supreme Court rejected a last-minute appeal.
The International Court of Justice had urged Texas not to execute Medellin, as he had not been told of his right to consular help when he was arrested.
Texas argued that its courts were not bound by the rulings of the ICJ.
Medellin was pronounced dead at 2157 on Tuesday (0257 GMT), the Texas Department of Criminal Justice said in a statement.
The Mexican government has sent a note of protest to the US state department, expressing "its concern for the precedent that (the execution) may create for the rights of Mexican nationals who may be detained in that country."
The ICJ had ordered that his case and those of 50 other Mexicans on death row be reviewed because they had not been informed of their right to consular assistance at the time of their arrest - a right under the 1963 Vienna Convention.
The state department said it was powerless to delay the execution, noting that the US Supreme Court had ruled in March that President George W Bush lacked the authority to intervene in the case.
"We have an indisputable international law obligation that conflicts with state law," said state department spokesman Kurtis Cooper.
"The Supreme Court ruled the president has neither the constitutional power nor the legislative authority to overturn the state rules."
Medellin's case dates back to 1993 when two girls, Jennifer Ertman, 14, and Elizabeth Pena, 16, were raped and murdered by six gang members in Houston.
Set up in 1946, the ICJ is the highest United Nations court
Medellin, who was born in Mexico but moved to the US as a child, was convicted of Miss Pena's murder and did not deny that he killed her.
But at the time of his arrest, police did not tell him that he could request assistance from the Mexican consulate.
In 2003, Mexico, which does not have the death penalty, filed a lawsuit at the ICJ on behalf of Medellin and 50 other Mexican nationals on death row in the US, saying they had not been informed of their right to consular assistance.
The court ruled in Mexico's favour, and ordered that their cases be reviewed.
Earlier this year, President Bush directed Texas to comply with the ICJ but the Supreme Court justices decided 6-3 that he had overstepped his authority.
Texas acknowledged that Medellin had not been told he could ask for help from Mexican diplomats, but argued that he had forfeited the right because he never raised the issue at trial or sentencing.
State officials also argued that it would not have made any difference to the outcome of the case.
Last month, in response to an urgent request from Mexico, the ICJ ordered the US to "take all measures necessary" to halt Medellin's execution.
But Texas judicial authorities said in response that the law in Medellin's case was "clear".
"Texas is not bound by the World Court but by the US Supreme Court, which reviewed this matter and determined that the convicted murderer's execution shall proceed," a statement from the attorney general's office said.