The vast majority of the city's roughly 300,000 Palestinians are expected to boycott the polls again, despite calls by a minority to use the elections to seize influence in a city under full Israeli control for decades.
Rami Nasrallah, director general of east Jerusalem's International Peace and Cooperation Center think-tank, sees little to gain from voting.
"I'm not willing to recognize the political rules of the game and to recognize or legitimize the Israeli occupation," he said.
Israel captured the city's east and the surrounding West Bank in the 1967 Six Day War, later annexing east Jerusalem in a move never recognized by the international community.
Palestinians claim it as the capital of their future state.
Palestinian voter turnout was less than one percent in the last local vote in 2013, according to the Palestinian Academic Society for International affairs.
Municipalities and local councils across Israel will hold polls on Tuesday.
In Jerusalem a small number of Palestinian candidates are running for the council, but others have dropped out after criticism, intimidation and legal issues.
One of those who withdrew was Aziz Abu Sarah, who had even announced his intention to run for mayor.
He said it was time for Palestinians to "rethink" their boycott, pointing out that over 50 years Israel had moved around 200,000 settlers into east Jerusalem.
"We are losing Jerusalem every day," he said during his campaign.
While he received support from both Palestinians and Israelis, he also faced a series of attacks and at one event was egged.
Like most Palestinian Jerusalemites, Abu Sarah has residency and not an Israeli citizenship.
He was later told by Israeli authorities that his status as a Jerusalem resident was "being checked" due to his travel and work abroad, he wrote on Facebook.
"Entrenched political interest groups on both sides hope to maintain the status quo, and will stop at nothing to prevent forward progress," Abu Sarah said as he dropped out of the race.
Among the Palestinians still in the race is Ramadan Dabash, who heads a list of six Arab candidates running for seats on the city council.
He has an Israeli citizenship and is a former member of the right-wing Likud party run by Prime Minister Benjamin Netanyahu.
A lot of his votes could actually come from Jewish voters, rather than fellow Palestinians.
Dabash said he wanted to be on the council in order to protect Palestinians, and denied it amounted to recognizing Jerusalem as Israel's capital.
Palestinians who have residency status rather than full Israeli citizenship cannot vote in general elections but can for the municipality, which is responsible for most Jerusalem schools as well as rubbish collection and other services.
"Palestinians pay more than 400 million shekels ($110 million) tax to the municipality," Dabash told AFP. "They receive less than 10 percent of the services."
Dabash said his mediation had helped prevent the demolition of dozens of homes in his neighbouhood of Sur Baher in east Jerusalem.
But Palestinian involvement in the elections has been rejected by the Palestinian Authority, which has limited self-rule in the West Bank.
"Any Palestinian should refuse to be a part of them. We will not accept Jerusalem as the capital of Israel," senior Palestinian official Saeb Erekat told AFP.
"What did the PA do for Jerusalemites?" Dabash shot back. "Did they build them hospitals?"
But in the streets of east Jerusalem there has been no sign of any election campaigning.
The four leading mayoral candidates all hold conservative views on issues regarding the area's Palestinian residents.
Trader Abu Yasser, from Jerusalem's Old City, summed up the views of many Palestinians, saying he wouldn't vote as the elections wouldn't change much.
"If the Palestinians in Jerusalem knew they would achieve something from these elections they would have gone against the PA's wishes and voted to get municipal services," he said.