A police spokesman said they had not received complaints of any irregularities.
"There has been some friction between representatives of some candidates but nothing of importance," Major Bashir Daajeh said on state television.
The IAF accuses the authorities of manipulating votes cast by military personnel who are taking part in voting for the first time in municipal elections.
"This is a massacre of democracy and a flagrant attack on the will of [the] people"
Zaki Bani Rusheid, head of the IAF
The party alleges the military voters are being directed toward urban centres where IAF candidates are running, casting votes in favour of rivals.
"This is a massacre of democracy and a flagrant attack on the will of (the) people," Zaki Bani Rusheid, head of the IAF, said after the party made its decision to withdraw its candidates.
"We credit the government with one point only - transparency in forging the elections without any window-dressing or make-up."
The IAF also said some votes had been cast more than once, and held the government responsible.
Bani Rusheid said the alleged irregularities may prompt the IAF to boycott Jordan's parliamentary elections, which are due to take place later this year.
Close to two million Jordanians are registered to vote in 1,980 polling stations across the kingdom to elect 965 municipal council members and mayors.
Nearly 2,700 candidates are running for council seats in 94 municipalities.
The vote is the first to be held since a new law was passed earlier this year granting women a 20 per cent quota and reducing voter age.
A total of 361 women are running for municipal jobs, including six who are seeking mayoral positions.
Thirty-three candidates, including independents, are running on an Islamic platform in the election, compared to 11 in 2003.
Polling stations were scheduled to close at 5pm on Tuesday, which was declared a public holiday to allow the largest number of people to vote.
However, voting was extended by up to four hours in areas where turnout was less than 50.1 per cent, officials said.
"A turnout of 50.1 per cent has not been achieved in three municipalities and in 12 areas of Greater Amman, and voting there has been extended," Nader Zuheirat, minister of municipalities, said.
Saad al-Manasseer, Amman's mayor, said that voting in his constituency was extended for a second time until 9pm, as turnout had only reached 48 per cent.
Voting could continue into Wednesday if the turnout is not deemed sufficient, officials said.