Riad Ras, Hassan Safi and Bassem Obeido were seized at gunpoint overnight under the cover of darkness in the towns of Tulkarem, Bethlehem and Hebron, respectively.
Ras, a lecturer at Al-Najah university in the northern West Bank town of Nablus, was released several hours after he was kidnapped late on Thursday.
In a statement sent to Palestinian media on Friday, the previously unheard of Omar bin al-Khattab Brigades claimed to have kidnapped the three men.
"It's our first retort to Hamas' dealings and its disregard for Palestinian law," said the group, named after one of the first Muslim caliphs and a companion of the Prophet Mohammed.
Mushir al-Masri, a Hamas spokesman, accused "certain circles in the Palestinian Authority" of having a hand in the kidnappings and talked about a "component extolling the eradication" of the Islamist group.
He said, without elaborating, that Hamas had "several options" in order to free its members provided they were not first released.
Long-standing tensions between Hamas and the ruling Fatah party have been exacerbated by Israel's pullout from the Gaza Strip, with fighters flatly refusing calls from Palestinian leader Mahmoud Abbas to disarm.
Israel's pullout from Gaza has
sparked an upsurge in violence
On 23 September, 16 people were killed in an explosion at a Hamas rally in the Gaza Strip. The group promptly blamed on Israel, which denied any involvement, before firing a slew of rockets into Israel.
Those attacks were met with Israeli air strikes that killed four Palestinian fighters, including two Hamas activists.
An official Palestinian investigation published on Monday concluded what a majority of Palestinians suspected, that the explosion was caused by a Hamas missile.
On Sunday, three people were killed, including a policeman, in the first deadly internecine strife in Gaza since Israel's pullout, as armed Hamas men clashed with security forces.
An umbrella group representing the main Palestinian factions on Wednesday criticised Hamas for its "armed aggression" during the clashes.