More than 400,000 Palestinians were eligible to cast ballots for representatives in 154 village councils in the West Bank, where Abbas’ Palestinian Authority has limited self-rule.
Municipal votes are typically held every four or five years.
Municipal elections are not being held in Gaza, whose rulers Hamas are boycotting the vote amid a rift with Abbas’ Fatah party.
The 86-year-old president postponed municipal votes in major West Bank cities, such as Ramallah, that could have been seen as a referendum on Abbas’ rule.
“These elections cannot be an alternative to legislative elections,” said Ahmad Issa, 23, outside a polling station in the West Bank village of Bir Nabala, adding that a legislative vote could offer “a horizon for the youth” and lead to reforms.
In the village of Beit Kahil, women and men lined up outside a polling station, some in facemasks to protect against COVID-19. Once inside, they placed voting papers in envelopes and dropped them into ballot boxes, dipping their fingers in ink as they left in a move to prevent people voting twice.
Abbas, whose support has sagged in opinion polls, drew widespread anger in April when he cancelled legislative and presidential elections scheduled for the summer, citing Israeli curbs on Palestinian voting in East Jerusalem.
Abbas’ rivals, including Hamas, accused him of using the Jerusalem voting dispute as an excuse to cancel elections that polls showed he and his party would lose to the group. Abbas, who has ruled by decree for over a decade, denies this.
A spokesman for Hamas, which boycotted previous municipal elections in 2012 and 2017, stated the group “refuses to participate in partial elections that are tailored to Fatah, and conducted by the Palestinian Authority”, calling on Abbas to reschedule the cancelled summer votes.
Hamas has enjoyed a surge in popularity in the West Bank and East Jerusalem since fighting an 11-day war with Israel in May. The group won student council elections this year at several top West Bank universities, an important barometer of support.
The Palestinians seek statehood in the West Bank, Gaza and East Jerusalem, territory Israel captured in a 1967 war. Israel annexed East Jerusalem in a move not recognised internationally, and peace talks between the two sides broke down in 2014.
Hamas won the Palestinians’ last legislative election in 2006. That victory laid the ground for a political rupture. Hamas seized Gaza after fighting a short civil war there with Fatah in 2007 and has ruled the coastal enclave ever since.