Javier Solana added on Wednesday that he doubted any progress to date had been made in promoting a world court dealing in international justice to Washington.
"The sentiments are very profound in the United States, that fellow citizens cannot be judged by a court that is not American.
"Maybe it is better not to keep on trying but to try to establish a modus vivendi, knowing that this is not going to be a possibility for the United States, for any president of the United States to change the position," he added.
The ICC was established in The Hague last year.
Many countries, including the 25 European Union states, have said they want it to cut its teeth by trying alleged war crimes and crimes against humanity arising from the Darfur issue in Sudan.
A United Nations-appointed commission has reported that all parties responsible for having committing serious crimes in Darfur should be tried by the ICC.
Frivolous casesBut Washington has been implacably opposed to the court from the outset, fearing "frivolous" cases being brought against US citizens, including soldiers serving abroad, for example in Iraq or Afghanistan.
The ICC is the world's first permanent war crimes court, and is based in the same city as the ad hoc International Criminal Tribunal for the former Yugoslavia (ICTY), established by a UN Security Council resolution in 1993 and due to wind up in 2008.
"I don't think we are going to make any progress"
EU foreign policy chief
Since Sudan itself is not a signatory to the ICC, and given the opposition of Washington, which is heavily involved in diplomatic efforts to end fighting in Sudan, it would take a Security Council resolution to decide how and where to try Darfur war crimes, Solana said.
"I think in this case they will be more inclined to use the left-over tribunal that was used for Rwanda," the EU foreign policy chief said, referring to an International Criminal Tribunal for Rwanda operating in the
northern Tanzanian town of Arusha.
A Rwanda tribunal is currently
hearing cases in Tanzania
"This is what the United States will probably defend in the Security Council," he added. "We will continue to defend the ICC and probably the compromise at the end will be to utilise the Rwandan tribunal."
The Rwanda tribunal is hearing cases following the massacre of 800,000 Tutsis and moderate Hutus from April to July 1994.