Lawyers for two US citizens accused of terrorism have told the Supreme Court that President Bush has no right to detain them as "enemy combatants".
Padilla is also known as Abdullah al-Mujahir
Jose Padilla was arrested over an alleged "dirty bomb" plot in Chicago while Yaser Hamdi was captured in combat in Afghanistan.
Lawyer Frank Dunham argued that Mr Bush was exceeding his authority by denying them access to lawyers and courts.
But a White House lawyer said the two men posed a national security risk.
Bush administration attorney Paul Clement said the government had the authority to hold "unlawful enemy combatants" to prevent them returning to battle.
The Supreme Court is not expected to issue its rulings until late June. Both men are being held without charge at a naval prison in South Carolina.
The BBC's Washington correspondent, Justin Webb, reports that these are truly historic cases with far-reaching implications for the liberty of Americans and the ability of the US government to lock up those of its citizens it considers to be a threat.
Lawyers say the fact that Mr Hamdi, born in Louisiana, was seized in a foreign war zone makes his case easier for the government to defend.
However, Mr Padilla was arrested at Chicago Airport, accused of plotting to set off a radiological weapon in an American city. No evidence has ever been brought before a court.
Nine justices will hear pleas from lawyers for the two accused and for the Bush administration.
The Supreme Court decided to hear the cases after a federal appeals court requested the release of Mr Padilla on the grounds that an American citizen could not be arrested in the US as an enemy combatant.
Mr Padilla was arrested in Chicago in May 2002 on suspicion of planning to set off a "dirty bomb".
One of his attorneys, Andrew Patel, said his client's rights had been ignored.
"He hasn't had a chance to defend himself," he said.
Attorney General John Ashcroft has said it is in the national interest to designate Mr Padilla as an enemy combatant as it has been determined that he is a grave danger to security.
He accused Mr Padilla of having close ties to al-Qaeda and argued that President George W Bush's authority to designate individuals as enemy combatants was a "vital part of the war on terrorism".