In a statement, the CIP said the time has come to begin pressuring Palestinian factions to set national priorities.
''It is unreasonable that the terms of the reconciliation [deal] are not applied on the ground,'' said Muhannad al-Rabi, a member of the CIP leadership.
The calls come as Palestinian officials plan on seeking statehood with the UN in September.
Rabi pointed out that the international movement has begun to dramatically escalate, which requires the Palestinians to unite behind one common purpose.
Factions in the once split Palestinian territories signed a unity deal in early May. Dissension over who would be prime minister of the interim government has stunted the process.
Another obstacle in the way of the deal is the ongoing political persecution of Hamas in the Fatah-ruled West Bank. The agreement stipulated the release of all political prisoners.
On Sunday, the Islamic Jihad party accused West Bank security services of summoning six of its elements for questioning in Kafr Ra'i in Jenin city.
Hamas has accused the security services of summoning its elements as well, and has issued repeated calls for the release of its supporters, calling their release a prerequisite for the unity deal.