ICC president Chile Eboe-Osuji called on the US to "join her closest allies and friends at the table of the Rome Statute", referring to the court's founding document.
"The past, present and future victims of genocide, crimes against humanity and war crimes need her to do so," Eboe-Osuji said in remarks made in the US capital on Friday, released by the court on Monday.
The United States has never joined the ICC, whose chief prosecutor Fatou Bensouda asked judges in November 2017 to authorise her to open a probe into alleged war crimes in Afghanistan.
Some legal experts say the case is the Hague-based court's most complex and politically controversial investigation to date. It could be the first time alleged crimes committed by US forces could be under the spotlight.
In response, US Secretary of State Mike Pompeo announced two weeks ago that they would deny visas to ICC members involved in any investigations into actions of US troops in Afghanistan or other countries.
It was the US's first concrete action against the ICC since the White House threatened reprisals against the tribunal in September last year.
But Eboe-Osuji said: "It is, with all due sense of responsibility that I directly request the leadership of the United States to give its support to the ICC."
The ICC is the world's only independent legal body set up in 2002 in The Hague to try the gravest of crimes such genocide, war crimes and crimes against humanity.
It can however only get involved when states are unwilling or unable to investigate themselves.
It is ruled by the Rome Statute and currently has 122 member states. Its chief prosecutor can initiate investigations on her own if the probe involves at least one member state —in this case Afghanistan.
Relations with various US administrations have been strained since the court started its work.
The US Congress in 2002 passed the American Service Members Protection Act, which contained a number of provisions should a US citizen ever be put before the ICC.
Also known as the "Hague Invasion Act," one provision within the federal law allows for the US president to authorise military force to free any US personnel held by the ICC.
- Countries: Africa