"We agree to suspend all military action inside Israel ... in order to support Abbas' political programme," said Zachariya Zubaidi, a leader in the brigades, an offshoot of Palestinian leader Mahmud Abbas' Fatah movement.
The pledge came after Abbas held a three-hour meeting with Hamas leaders in Gaza Strip on Tuesday.
Palestinian public security chief Major-General Abd al-Razak al-Majaydah said on Wednesday an "arrangement is under way to deploy national security forces on the borders within two days to prevent violations".
Wail al-Dauduh, Aljazeera's correspondent in the West Bank, said the most important topic of discussion was the possibility of a reaching a ceasefire between Palestinians and Israelis.
He said the meeting also discussed the Palestinian political partnership and guarantees Abbas may offer to Hamas and other factions to ensure that Israel would not continue its assassinations, raids and targeting of the factions if a truce was agreed to.
"Calm was one of the points raised in the meeting within the framework of stabilising the Palestinian situation. We have listened to Abu Mazin (Abbas) and we will study the issue within the movement," said Sami Abu Zuhri, a Hamas spokesman in Gaza.
"Both sides expressed their mutual interest to achieve the interests of our people and maintain national unity," he said. "Further meetings are expected in coming days."
"Both sides expressed their mutual interest to achieve the interests of our people and maintain national unity."
Sami Abu Zuhri,
Al-Dauduh said the meeting had achieved more progress than previous meetings between the two sides but cited officials as saying that more meetings were needed to reach agreement.
The talks are part of a series of meetings Abbas aims to hold with Palestinian faction leaders and security officials in Gaza in an attempt to halt operations inside Israel.
Israel has threatened a broad Gaza offensive to stop attacks but hinted Abbas would be given time to act beforehand.