"The commission has to act expeditiously in order to seriously address all complaints," the UN's envoy to Iraq, Jan Kubis, said in a statement.

Partial results for the May 12 poll show the Marching Towards Reform alliance of Shiite cleric Moqtada Sadr and communists ahead in six of Iraq's 18 provinces and second in four others.

Preliminary tallies also put the Conquest Alliance of pro-Iranian former paramilitary fighters who helped battle IS next, followed by incumbent Prime Minister Haider al-Abadi's bloc.

But the exact number of seats won by each bloc in parliament is still unknown.

The United Nations cited partial recounts in some locations, including Kirkuk.

"It is important these are undertaken in full transparency, witnessed by stakeholders, to strengthen... confidence in the process," said Kubis.

Several complaints have been lodged in Kirkuk, a multi-ethnic province which the central government has recently taken over from the Kurds.

Disputes between Kurdish, Arab and Turkmen communities led to a curfew being imposed in Kirkuk city on the night of the vote, with clashes and sit-in protests.

"I also call on all political actors to uphold the peace and to remain committed to resolving any electoral disputes through the established legal channels," Kubis added.

Former prime minister Nuri al-Maliki, whose Rule of Law Alliance falls behind the top three blocs in the partial results, has called for the commission to recount votes or cancel the elections.

The vote, the first in Iraq since the government declared victory against the Islamic State group in December, is also the first to have taken place without significant political violence since the US-led invasion that toppled Saddam Hussein in 2003.