Ban Ki-moon, the UN secretary general, had called on the US to abide by an International Court of Justice (ICJ) ruling to stay Medellin's execution.
The ICJ had said that Medellin and about 50 other Mexicans on death row in the US should have new hearings to determine whether the Vienna Conventions were violated during their arrests.
Medellin's lawyers said he was denied access to Mexican consular officials during his arrest, a key part of the conventions
He was the first among the 50 to be executed.
|Medellin is set to be executed on Tuesday [AFP]
The US embassy in Mexico ha warned of potential protests there if the execution took place.
Jorge Montano, a former Mexican ambassador to the US, told Al Jazeera that the US should respect international law.
"The biggest lesson once again for the rest of the world, the US is not prepared to respect any ruling when that ruling is not in their favour and that, for me, is like the law of the jungle once again. If we don't respect the international legislation, then how can we ask other countries to do so?"
George Bush, the US president, has asked states to review the cases affected by the ruling, but the US Supreme Court ruled earlier this year that neither the president nor the international court can force the Texan state government's hand.
David Fathi, the US programme director from the Human Rights Watch group, told Al Jazeera that the decision to go ahead with the execution had grave implications for US citizens possibly facing execution abroad.
The US would find it difficult to say other countries should honour their obligations not to execute US citizens when the US has itself violated international law, he said.
Medellin was the fifth Texas inmate to be executed this year.
Trial testimony showed Medellin was the first of six members of a street gang to attack the girls when the incident took place in 1993.
Sixteen year old Elizabeth Pena and 14-year-old Jennifer Ertman were taking a shortcut home across a railway bridge in Houston, Texas.
The gang attacked the girls for an hour before strangling them and leaving their bodies to decompose in a field.