The IDF said the claim was being verified.
A spokesman for the cell told Ynet that members of the group had fired a 'Bashaar 1' rocket a 7:20 pm Wednesday night. He also said that the organization intends to continue manufacturing rockets in the West Bank as a response what he called the ongoing "Israeli crimes against the Palestinian people."
The spokesman added that the rocket launching was a response to reports that the Palestinian Authority plans to dismantle the al-Aqsa Martyrs Brigades.
"We are obligated to the path of the (armed struggle), the Fatah movement's path. We won't put our guns down and we'll continue resisting the occupation. Our weapons will continue to be steadfastly pointed towards the Zionist enemy."
This is not the first time that the group has tried to launch rockets towards Israeli settlements in the West Bank. About a year ago, there were two incidents in which Palestinians claimed to have attempted to fire rockets from the northern West Bank into Israel.
On one occasion, Palestinians claimed that a rocket was fired from Jenin towards an Israeli settlement bloc. The IDF responded that it had not found any indication a rocket had been launched.
A few days before the supposed Jenin launch, an attempt to fire a rocket from Tulkarm apparently failed.
Spokespersons for various Palestinians groups, primarily from the Popular Resistance Committees, have said in the past that they are seeking to begin firing rockets from the West Bank into Israel.