TRIPOLI, Oct 24 (Reuters) - Registration for candidates in Libya"s presidential and parliamentary elections should open in November, the head of the electoral commission said on Sunday. Elections are a key step in a U.N.-backed process to end a decade of violence by creating a new political leadership whose legitimacy is widely accepted. But wrangling over the constitutional basis for elections, the rules governing them and questions over their credibility have threatened to unravel the peace process in recent months. The first round of the presidential election is due to be held on Dec. 24. A second round, along with a parliamentary election, will then be held at a later date, said the commission head, Emad al-Sayah. He said the registration process should open by mid-November, after technical and logistical preparations were complete. But the complexities of the political patchwork resulting from divisions between eastern and western Libya mean there are still hurdles to overcome. Although parliament has issued a law enabling the presidential election to be held on Dec. 24, it has also issued another law saying the parliamentary election will happen separately, at a later date. Other political institutions have rejected parliament"s proposals. Eastern commander Khalifa Haftar paved the way to stand as president by saying in September he would step down from his military role for three months. Haftar heads the eastern-based Libyan National Army (LNA) and waged war on western factions after the country split in 2014. His 14-month offensive to take Tripoli, in the west, devastated areas of the capital but was repelled last year. Aides to parliament head Aguila Saleh said he had also stepped down from his position in order to run in the election. People close to Saif al-Islam Gaddafi, son of the late ousted leader Muammar Gaddafi and once the second most powerful man in Libya, have signalled that he also wants to compete.