Former US President Jimmy Carter offered Thursday to monitor Lebanon's parliament elections next year - a vote that will be fiercely contested between the militant Hizbullah group and its rival pro-Western parties. Carter proposed a monitoring mission by his Atlanta-based Carter Center during a Beirut meeting with the interior minister, Ziad Baroud, who welcomed the offer but said the Cabinet must approve it. The vote has to be held between April 20 and June 20, though no specific date has been set. The interior ministry is in charge of organizing and overseeing the elections. Carter also met members of parliamentary blocs, but he did not meet with lawmakers from Hizbullah. The Shi'ite terror group is on the US State Department's terrorist list. Carter said he is ready to meet with Hizbullah but they refuse to meet current or former US presidents. The vote is crucial for both the Western-backed anti-Syrian groups that hold majority seats in the current 128-member parliament and the Hezbollah-led coalition backed by Syria and Iran seeking to take over. Carter told reporters after meeting Baroud that his center "looks forward with great anticipation" to the mission, if approved by the government. "We have nothing to hide," Baroud said. "On the contrary we are working in a very transparent way. We want these elections to be held in the best form." Still, Carter met with some Hizbullah allies, including Christian leader Michel Aoun and members of parliament Speaker Nabih Berri's bloc. After Lebanon, where he arrived Tuesday, Carter is heading to Syria on Saturday. In the Syrian capital of Damascus, a senior Hamas official said that the former US president will meet the terrorist Palestinian group's exiled leadership on Sunday. The official said Carter would discuss with Hamas officials the fate of Israeli soldier Gilad Schalit, who was captured by Hamas-linked terrorists near Gaza in 2006 and held hostage since. A possible truce between Hamas and Israel will also be on the agenda. Carter was widely criticized in April when he met in Syria with the exiled Hamas leader, Khaled Mashaal. The US also labels Hamas as a terrorist organization. The Mashaal-Carter meeting led to the delivery of a handwritten letter from Schalit to his parents.