Updated

As the lethal injection began taking effect, the Mexican National convicted of the brutal rape and killing of a teenage girl in 1995 shouted, "Viva Mexico!" just before he died at a Texas prison.

Efforts by Humberto Leal's attorneys to halt the execution fell short, with the U.S. Supreme Court turning back a stay request and Texas Gov. Rick Perry refusing to grant a pardon. He was pronounced dead at 6:21 p.m. local time.

In his last minutes, Leal repeatedly said he was sorry and accepted responsibility.

"I have hurt a lot of people. ... I take full blame for everything. I am sorry for what I did," he said in the death chamber.

"One more thing," he said as the drugs began taking effect. Then he shouted twice, "Viva Mexico!" at a Texas prison.

President Obama, the State Department and Mexican authorities asked Texas for a last-minute reprieve, citing the U.N.-enforced 1963 Vienna Treaty, which requires foreign nationals who are arrested in foreign countries the right to access their consulates.

The U.S. Supreme Court denied Leal's request, calling his argument meritless.

In a 5-4 decision an hour before the execution, the majority wrote, “We have no authority to stay an execution in light of an 'appeal of the President,' presenting free-ranging assertions of foreign policy consequences, when those assertions come unaccompanied by a persuasive legal claim.”

After the decision, Sandra L. Babcock, an attorney for Leal, issued a statement linked to Twitter, saying her client will "suffer the consequences" of the U.S. stumbling on its commitment to rule of law.

"He will be executed tonight," she writes."Despite the fact that his right to consular assistance was violated."

Leal, who moved to the U.S. as a toddler, contended police never told him he could seek legal assistance from the Mexican government under the treaty -- and that such assistance would have helped his defense.

Details of the murder were particularly gruesome.

Adria Sauceda, 16, his victim, was found naked by authorities, according to court documents.

"There was a 30- to 40-pound asphalt rock roughly twice the size of the victim's skull lying partially on the victim's left arm," court documents read. "Blood was underneath this rock. A smaller rock with blood on it was located near the victim's right thigh.”

A "bloody and broken" stick roughly 15 inches long with a screw at the end of it was also protruding from the girl's vagina, according to the documents.

In his first statement to police, Leal said Sauceda bolted from his car and ran off. After he was told his brother had given detectives a statement, he changed his story, saying Sauceda attacked him and fell to the ground after he fought back. He said when he couldn't wake her and saw bubbles in her nose, he got scared and went home.

Last Friday, the Obama administration asked the U.S. Supreme Court to stop Texas from executing Leal, asking the court to delay the execution for up to six months to give Congress time to consider legislation that would enforce the U.N. treaty.

Congress had three years to pass the bill but did not. Hence, it was impossible to pass a bill that would spare Leal unless a stay is ordered.

Mexico's foreign ministry said in a statement that the government condemned Leal's execution and sent a note of protest to the U.S. State Department. The ministry also said Mexican ambassador Arturo Sarukhan attempted to contact the Texas governor, who refused to speak on the phone.

The governor's office declined to comment on the execution Thursday, but his office appeared to bristle at the idea of an international body influencing the state's sovereignty.

For 16 years, Leal has exercised his right to file appeals and motions so extensively, one judge in federal district court called his case "one of the most procedurally convoluted and complex habeas corpus proceedings" he ever reviewed.

Meanwhile, in San Antonio, Adria's father, Rene Sauceda, reportedly begins each morning by reading a South San Antonio High School newspaper clipping from May 25, 1995 -- just after the first anniversary of his daughter's death.

"I look at that every day," Sauceda, 64, told the San Antonio Express-News.

FoxNews.com's Edmund DeMarche and The Associated Press contributed to this report.