The man, from Co Louth, appeared via videolink from police custody before a district judge in Belfast on Saturday morning.
As well as a count of child abduction, he is also charged with possession of an indecent image and several motoring offences.
The man was detained earlier this week after he and the teenage girl were found together in Northern Ireland.
Representing the accused, solicitor Sophie McClintock said her client was in full employment, had no criminal record and had the full support of his family.
“His family are extremely supportive of him,” she said.
A police officer objected to bail amid concerns the man would not return to Northern Ireland to face legal proceedings if he was allowed to return home to the Irish Republic.
The court was told a picture found in the accused’s wallet had been classified as a “category A” indecent image.
Ms McClintock said the accused’s parents were willing to offer a £5,000 cash surety as an assurance he would return to court. She said the accused was also willing to offer 4,000 euro.
District judge Amanda Henderson granted bail with a number of conditions.
Those included £500 bail from the accused and a further £5,000 cash surety, that he is to reside at an address agreed by the Police Service of Northern Ireland, that he surrender his passport and that he have no contact whatsoever with the alleged victim.
The case was listed for a further hearing on May 4.