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No one disputes that a U.S. Border Patrol agent shot and killed an unarmed 15-year-old near the border that separates El Paso, Texas from Juarez, Mexico.

The agent was on the U.S. side of the border. The boy, a Mexican national, was on the other. On Tuesday, the U.S. Supreme Court considered whether his parents can sue the agent for killing their son.

Based on their questions, the justices seemed to indicate the answer would be no. The court appeared headed for a tie, and would order the case to be reheard if Neil Gorsuch is confirmed, which would bring the court back to full strength.

Attorney Randolph J. Ortega addresses the Supreme Court in Hernandez v. Mesa on Feb. 21, 2017. Art Lien

The case comes at a time of heightened tension between the U.S. and Mexico over President Trump's insistence that Mexico eventually pay for completing a wall along the border.

The Mexican government, in a brief filed in the case, said it has an obligation to see that the agent is held accountable and the victims are compensated.

"The United States would expect no less if the situation were reversed and a Mexican government agent, standing in Mexico and shooting across the border, had killed a US national."

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In June of 2010, Sergio Hernandez Guereca was playing with three friends in the cement culvert that separates the two cities. The boys dared each other to cross the unmarked border, run up and touch the fence on the U.S. side, then run back to the Mexican side.

A U.S. Border Patrol agent, Jesus Mesa Jr, arrived and detained one of them, but Hernandez ran away, making it back to the Mexican side. Agent Mesa drew his weapon and fired from about 60 feet away, hitting the 15-year-old with a fatal shot to the head.

Attorney Robert C. Hilliard addresses the Supreme Court in Hernandez v. Mesa on Feb. 21, 2017. Art Lien

An investigation by American authorities concluded that Mesa fired in self-defense, because smugglers were throwing rocks at him, though it found no evidence that Hernandez threw anything.

Mexican prosecutors charged Mesa with murder.

When the U.S. refused an extradition request, the parents sued. But American courts threw their case out, concluding that the Constitution's protection against excessive force does not apply to someone who is outside the United States.

Agent Mesa urged the Supreme Court to follow the reasoning of a 1990 case in which the court ruled that constitutional rights applied only inside the nation's borders unless a person had "a significant voluntary connection" to the US.

The Supreme Court Building on Capitol Hill. Karen Bleier / AFP - Getty Images

But the boy's parents argued that the court should instead look to its more recent ruling in a 2008 case involving detainees at Guantanamo Bay. That decision said courts should be more flexible in deciding when and where U.S. constitutional rights apply.

A loss for the parents, their lawyer argued, would create "a legal no-man's land in which federal agents can kill innocent civilians with impunity."

Some of the court's more liberal justices seemed to agree during Tuesday's courtroom argument. Stephen Breyer said the cement culvert is jointly maintained by the U.S. and Mexico, making it a special area where the U.S. Constitution should apply.

But the court's conservatives repeatedly pressed the lawyer for the family to lay out a definite rule on when someone outside the US should be able to sue, claiming use of excessive force.

"How about the case of a drone strike in Iraq?" asked Chief Justice John Roberts.

And Anthony Kennedy, who may hold the deciding vote, said cross-border incidents should be resolved by Congress and the State Department, not the courts. "This is a critical area of foreign affairs," he said.

The court appeared to be headed for a 4-4 tie, which would be a loss for the parents, because it would leave intact the lower court rulings against them. It could issue a ruling with a tie or hold the case for later reargument.

A ruling is expected by late June.