The United States Supreme Court appears to be evenly split over the rights of a Mexican family to use American courts to sue a US Border Patrol agent who fired across the border and killed their teenage son.

Key points: Sergio Hernandez was shot while on the Mexican side of the US-Mexico border by a US Border Patrol officer standing on US soil

Sergio Hernandez was shot while on the Mexican side of the US-Mexico border by a US Border Patrol officer standing on US soil Hernandez' family is seeking to sue the officer, saying he violated their son's constitutional rights

Hernandez' family is seeking to sue the officer, saying he violated their son's constitutional rights Supreme Court justices appears split over whether to hear the case after it was dismissed by a lower court in 2014

In the closely watched case that could affect US immigration actions under President Donald Trump's administration, the court's liberal justices expressed sympathy towards allowing the case to move forward, while the conservative justices expressed scepticism about reviving the lawsuit, indicating they could be headed towards a 4-4 split.

Such a ruling would leave in place a lower court's decision to throw out the civil rights claim against the agent, Jesus Mesa, filed by the family of Sergio Adrian Hernandez Guereca.

The case arose from an incident that took place in June 2010 in the cement drain that separates El Paso, Texas, from Ciudad Juarez, Mexico.

The circumstances of exactly what occurred are in dispute, but what is clear is the agent was on the US side of the border when he fired his gun, striking Hernandez on the Mexican side.

Justice Anthony Kennedy, a conservative who sometimes sides with the liberal justices in close cases and whose vote could be pivotal in this one, voiced doubt over the family's arguments during the court's hour-long argument.

He and other conservative justices suggested the boy's death on the Mexican side of the border was enough to keep the matter out of US courts.

The four liberal justices indicated they would support the parents' suit because the shooting happened close to the border in an area in which the two nations share responsibility for upkeep.

Mexican police watch as US border agents stand in a cement drain between El Paso, US and Ciudad Juarez, Mexico. ( Reuters: Alejandro Bringas )

Case raises constitutional law questions

The case raises several legal questions, including whether or not the US constitution's ban on unjustified deadly force applied to Hernandez because he was a Mexican citizen on Mexican soil when the shooting occurred.

The court could resolve the case by deciding not to apply a 1971 Supreme Court ruling in a case involving federal drug enforcement agents that allowed such lawsuits in limited circumstances. The court has been reluctant in subsequent cases to extend that ruling to other types of conduct.

Justice Kennedy seemed unwilling to take that step, saying the Hernandez shooting would be an "extraordinary case" in which to allow a lawsuit against a federal official.

Liberal justices appeared more willing to examine whether some US rights extend to border areas where the US Government exercises a certain amount of authority even beyond the border line, as it does in the drain where Hernandez was killed.

In the case of a 4-4 tie, the Supreme Court could potentially delay action on the case to see if Mr Trump's nominee to fill a vacancy on the court, conservative appeals court judge Neil Gorsuch, is confirmed by the US Senate.

Judge Gorsuch could then potentially cast the deciding vote.

The US Border Patrol has said Hernandez was pelting US agents with rocks from the Mexican side before the shooting.

US authorities have asserted that Mr Mesa shot Hernandez in self-defence.

Lawyers for Hernandez's family disputed that account, saying he was playing a game with other teenagers in which they would run across a drain from the Mexican side and touch the US border fence before dashing back.

The justices heard the case at a time of interest in the security of the lengthy US-Mexico border, with Mr Trump moving forward with plans for a border wall he said was needed to combat illegal immigration.

AP/Reuters