The International Criminal Court in April rejected a demand by its chief prosecutor to investigate crimes committed in the war-torn nation since 2003 -- a probe that has been bitterly opposed by Washington.

"This is a historic day for accountability in Afghanistan," said Fergal Gaynor, a lawyer representing 82 victims, adding that ruling out an investigation "without exaggeration, denies victims everything".

President Donald Trump's administration has strongly rejected any probe into Afghanistan. The United States has refused to join the ICC and accuses the court of trying to impinge on national jurisdiction.

Earlier this year it revoked the visa of the ICC's chief prosecutor, Fatou Bensouda, while then-national security advisor John Bolton warned last year that the United States would arrest ICC judges if it pursued the Afghan probe.

Trump's personal lawyer Jay Sekulow -- attending the hearing in what he said was an independent capacity -- told the Hague-based court that "the US is both willing and able to prosecute its own cases.

"There's no doubt about it. This is a direct move by the (ICC's) prosecutor on US interests," Sekulow later told reporters.

Sekulow said he was "defending the rights of US soldiers" on behalf of the Christian-based American Centre for Law and Justice.

The court allows numerous parties with a potential legal stake in the case to address it.

But he said he was not there "at the behest of the president or representing the United States."

- 'Horrendous torture' -

ICC prosecutors opened a preliminary investigation as far back as 2006 into war crimes and crimes against humanity committed in Afghanistan, and Bensouda requested a full-blown probe in 2017.

But judges turned down her request in April, saying it "would not serve the interests of justice" and that the court should focus on cases with a better chance of success.

Wednesday's hearings, the first of three days of proceedings, opened with technical arguments to decide whether victims would be allowed to take part in the appeal.

Rights groups denounced April's decision to block an investigation as a blow for thousands of victims in the long-running conflict, warning that impunity could embolden perpetrators around the world.

Prosecutors not only wanted to examine alleged crimes by the Taliban and Afghan soldiers but also by international forces, including US troops and the CIA.

Lawyers representing victims, some still being held by the US at its Guantanamo base, told the judges their clients wanted justice after suffering "years of horrendous torture."

One lawyer, Nancy Hollander, described how her client was abducted in 2003 and subjected to tortures including being stripped naked, sexual abuse and waterboarding.

"Not a shred of operational intelligence was ever gained by the torture of these people," she said.

The United States has never ratified the ICC's founding Rome Statute and has been at loggerheads with the ICC since it opened its doors in 2002.

Afghanistan's government has also filed papers to the court opposing any probe.

"After more than four decades the people and government of Afghanistan want justice. But it is our own responsibility to bring justice for our nation and for our people," Kabul's ambassador Homayoon Azizi told reporters outside the ICC.