The gunfire in Karachi on Monday night was celebratory
Voting explained
They are confident supporters of President Pervez Musharraf are heading for a heavy defeat.
Early unofficial returns suggest some of the president's allies have lost their seats, but it is expected to be some time before a clear trend emerges.
Polling was delayed after the killing of opposition leader Benazir Bhutto.
On the streets of Karachi, young supporters of Ms Bhutto's PPP party celebrated late into the night, dancing and firing guns into the air, says the BBC's Jill McGivering.
But across the city, their main political rivals, allies of President Musharraf, were also claiming victory, our correspondent adds.
Most official counts will not be declared until later on Tuesday.
Street protest threats
A number of people were killed in clashes between rival party supporters during Monday's election, and there were reports of missing ballot boxes.
But there was also widespread relief that there were none of the major bomb attacks which had marred the run-up to the election.
Fears of violence had dissuaded many of the country's 80 million eligible voters from leaving their homes, and voter turnout was estimated to be less than 40%. Close to half a million security personnel, including about 80,000 soldiers, had been deployed to quell any outbreak of fighting.
Former Prime Minister Nawaz Sharif accused the PML-Q party that backs Mr Musharraf of fixing votes and attacking supporters of his PML-N party in some areas.
Asif Ali Zardari, Ms Bhutto's widower and the leader of her PPP party, had threatened to launch street protests if the election was rigged.
One international election observer, US Senator Joseph Biden, said he feared instability if electoral malpractice was suspected.
"If the majority of Pakistani people do not think the election was fair then I think we have a real problem," he said.
No clear majority
For his part, Mr Musharraf, who voted in Rawalpindi, vowed to work in "harmony" with whoever won Monday's election.
HAVE YOUR SAY The difficulty is in foreseeing what changes will come. Briscott, Pakistan
Polls suggest a fair vote is likely to result in a hung parliament, with none of the three biggest parties winning a majority, analysts suggest.
Attention will then turn on the PPP, and whether it chooses to join forces with pro-Musharraf parties, or with Mr Sharif's party.
Mr Sharif is staunchly opposed to the president, and if the two opposition parties jointly gain two-thirds of the seats, they may try to impeach Mr Musharraf, correspondents say.
Mr Musharraf stepped down as army chief late last year. He has ruled the country since seizing power in a coup in 1999.
Early poll results have shown that the anti-Musharraf parties,  and , are emerging as victorious. 
The early results also show that , the party supporting Pervez Musharraf, has been defeated.

Furthermore, the results for Pakistan's  indicate that the Pakistan Peoples Party currently have a small lead with 78 seats, with 's party just behind with 72 seats. The party which wins the elections for the National Assembly will choose the Prime Minister of Pakistan.
 
The elections had a slow start at 8 a.m. (0300 GMT), as fears of violence kept many voters away. To enforce security, the Pakistani police is backed up by some 80,000 troops. The BBC reported that 80 million people are eligible to vote, but many are expected to stay at home, largely because of fears about security. Authorities reported at least five explosions that had taken place on election day, all but one of which occurred near a polling area.