State Department spokeswoman Marie Harf said Washington had urged Texas authorities to look again Edgar Tamayo Arias' case, as he had been denied access to Mexican consular assistance.
"The department regrets Texas' decision to proceed with Mr Tamayo's execution without that review and reconsideration," Harf said, after a diplomatic outcry from Mexico.
Tamayo, now 46, was executed yesterday in Huntsville, Texas for the 1994 murder of a US police officer.
Mexico protested that his execution was illegal under international law, as he should have been accorded access to Mexican consular support at the time of his arrest and subsequent trial.
In 2004, the International Court of Justice ordered the United States to conduct judicial reviews of the convictions and sentences of Tamayo and 50 more Mexicans denied consular assistance.
Harf said that the United States remains bound by the Vienna Convention on Consular Relations, which also provides protection for US citizens arrested abroad.
"The Department of State had communicated these important interests to Texas authorities with respect to Mr Tamayo's case, including urging Texas to delay Mr Tamayo's execution," she said.
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