In a statement on Monday, the three groups said: "The occupation will not get any information about the missing soldier, except after committing to first immediately release all women prisoners from Israeli prisoners.
"Secondly, [we demand] the immediate release of all children under 18 years."
Monday's statement was issued in the name of the Izz al-Din al-Qassam Brigades, the armed wing of Hamas, the Popular Resistance Committees and the previously unknown Army of Islam faction.
Earlier on Monday, families of Palestinians jailed in Israel demonstrated in Gaza to demand that resistance fighters holding an Israeli soldier hostage trade him for the release of their relatives.
The call could complicate diplomatic efforts to free Corporal Gilad Shalit, 19, who was seized on Sunday when armed men from the ruling Hamas movement and other groups raided an army post near the southern Gaza Strip.
Israel has ruled out freeing any of the 9,000 Palestinians in its jails and threatened a military offensive in response to the attack.
Prisoners jailed for fighting Israel are widely seen as heroes by Palestinians.
"Kidnap one soldier and free 100 prisoners," chanted parents, friends and relatives of prisoners at a rally in Gaza on Monday.
"I call on the fighters ... not to let the soldier go. Hold him by your hands and teeth and free our sons," said Ghalya Baroud, whose son Ibrahim, a member of Islamic Jihad's armed wing, has spent more than 20 years in an Israeli jail.
The families criticised Palestinian and Egyptian efforts to free Shalit.
"Where were they when Palestinians were arrested? Where were they when innocent families were eliminated," Baroud said.
Hamas and other resistance groups have said in the past they would kidnap Israelis to try to gain the release of comrades imprisoned in Israel.
"Where were they when Palestinians were arrested? Where were they when innocent families were eliminated"
mother of jailed Palestinian
No group has claimed responsibility for holding the soldier nor have any demands been made.
"Kidnapping soldiers is the only way to free our prisoners," said Nabil al-Mansi, who was jailed for 11 years as a member of Hamas's armed wing and is now on a committee dedicated to the prisoners.
"It would be a stigma on the forehead of anyone who releases the soldier ... regardless of the price, even it were the heads of the Hamas leaders themselves."
Hamas, which refuses to recognise Israel, took over the Palestinian government in March after winning elections in January.