Abbas, during their meeting, urged an end to internal divisions among all Palestinian factions, and called for reconciliation to pave the way for the general elections in the Palestinian territories, according to the Palestinian news agency "Wafa."
Carter arrived in the Palestinian territories on Thursday leading a senior delegation of Council of International Wise Men. He was scheduled to pay a visit to Gaza and meet with Hamas movement officials, but the trip has been called off, Xinhua reported.
Abbas called on Hamas to enable the consensus government formed in June last year to perform its duties in the Gaza Strip and prepare for holding the general Palestinian elections.
Last week, the consensus government accused Hamas, which took control of the Gaza Strip by force in 2007, of obstructing it from unifying the official establishments of the Palestinian National Authority (PNA).
The government was formed in accordance to a deal, signed in Gaza between Hamas and Abbas Fatah Party in June; however, the government complains that Hamas refuses to help enable its effective rule.
The report said Abbas briefed Carter and his delegation on the recent development in the Palestinian territories and in the Middle East peace process, mainly Israeli governments refusal to abide by the international resolutions.
Meanwhile, Carter said he discussed with Abbas a series of essential questions including the current situation and the future of the Palestinian people.
"We came here to represent the hopes of the Palestinian people, therefore we hope to see that holding the Palestinian elections in Gaza, West Bank and Jerusalem will be an important step for them," said Carter.
He said the delegation discussed implementing last Aprils reconciliation deal reached in Gaza between Hamas and Fatah, adding "our council will exert all its efforts to implement this agreement."