The Arab administration promised to bring the men back before the court in Coleraine, Co Derry, if bail was granted, district judge Richard Wilson was told.
He later released the three men on combined bail and sureties of £5,500 (€7,000) each.
They have to make weekly contact with the Jordanian embassy in London before their next appearance in court on Oct 18.
Two wheelchair-using power-lifters — one a bronze medal winner at the Beijing Games — and a trainer have been accused of a series of charges, including sexual assault and voyeurism, following complaints by two girls and two women in Antrim.
The Jordanian team has been training in the town, about 22 miles from Belfast, in advance of the Paralympic Games starting next week.
The three were detained on Monday for questioning by detectives from the Police Service of Northern Ireland (PSNI).
A representative of the Jordanian government, counsellor Rulan Samara from the London embassy, told the court: “His majesty the King of Jordan (King Abdullah the Second) was inquiring about the matter and was asking about all the details.”
She promised the accused would be brought back for future court appearances in Northern Ireland by her government and offered a surety.
Power lifter Omar Sami Qaradhi, 31, lives in Barbados. He faces three charges of sexual assault, two against a child, and one of voyeurism after allegedly entering a women’s changing room at the Antrim Forum leisure centre.
Trainer Faisal Hammash, 35, is accused of inciting two girls to engage in sexual activity.
Power lifter Motaz Al Junaidi, 45, who won bronze at the last Paralympics in Beijing, is accused of sexual assault.
In granting bail, the judge said the embarrassment over a non-appearance would greatly outweigh the monetary loss.