In the two days before voting, at least eight people, including a communist candidate and several Maoists, were shot dead.
There have also been a string of small bomb attacks in the capital and the ethnically-tense south of the country.
Bhoj Raj Pokhrel, the chief election commissioner, said officials were "all concerned regarding election day violence".
Maoists attempted on Thursday to take over a polling station in the central town of Galkot, before setting it alight, an area official said.
Bhawani Prashad Parjuli said that police arrested 15 men after the attack, confiscating three grenades and a knife.
Maoist leaders in Kathmandu said they were investigating the report and that there was no effort under way to undermine the election.
An election candidate in the southern town of Janukpur was shot at by men riding a motorcycle, but she escaped unhurt, a district officer said.
Voting was also suspended at three stations in Chitwan, a southern district, after scuffles among party representatives, Ratna Raj Pandey, a district officer, said.
Jane Dutton, Al Jazeera's correspondent in Kathmandu, reported that travel bans and a ban on the sale of alcohol were being imposed during the polls.
Pushpa Kamal Dahal, alias Prachanda, the Maoist leader, called on his party activists to remain calm during polling.
"The need of the hour is to show restraint and have a fair and free election," he said in a statement after meeting Girija Prasad Koirala, the prime minister.
Prachanda has accused security forces of plotting to undermine the elections in order to save King Gyanendra from losing his throne.
The assembly's first tasks will be to abolish the 240-year-old Hindu monarchy and rewrite the constitution.
Gyanendra, viewed by some supporters as the incarnation of the Hindu god Vishnu, the protector, made a rare public statement.
"We call upon all adult citizens to exercise their democratic right in a free and fair environment," he said.
Tucked into the Himalayas between China and India, Nepal occupies an area of 147,000 sq km, with a population of 26.4 million
Nearly one-third of its people live on an income of less than a dollar a day
Eighty per cent of Nepalis are Hindus
Nepal was the world's last Hindu kingdom before declaring itself officially secular in 2006
In the latest death of the campaign, one protester was killed when police opened fire on demonstrators angry at the slaying of an election candidate the previous day.
Ram Kumar Khanal, an area police chief, said the police had opened fire with live ammunition in order to disperse protesters who were smashing stores and buses.
Election officials in Surket district, where Rishi Prasad Sharma, a member of the Communist Party of Nepal United Marxist Leninist was killed, postponed voting in Thursday's elections.A new polling date will be chosen in about a week for the constituency in Jahare Bazar town, Binod Kumar Pokhrel, an election official, was reported by The Associated Press as saying.
On Tuesday, six former Maoist rebels were shot dead by police during clashes with supporters of the rival Nepali Congress party in Dang district, 300km west of Kathmandu
Campaigning has also been marred by reports of intimidation by Maoist loyalists, many of whom have failed to adapt to civil life after years spent fighting government forces.
The United Nations, monitoring the elections and peace process, says Maoists have intimidated voters and prevented campaigning in some areas.
Other parties, it says, have also used violence and misused state machinery to influence voters.
The UN said it was "deeply shocked" by the election-related deaths, while election observers from the European Union spoke of their "deep concern" about the violence.
"The post-poll period will likely be difficult and dangerous," the International Crisis Group, which monitors security issues in different countries, said in a report.
"Parties will trade allegations of fraud and violence. The behaviour of powerful losers will shape the immediate aftermath."
The elections are the first since a peace deal brought Nepal's Maoists fighters into mainstream politics and ended a decade-long civil war in which at least 13,000 people have died.
The 27 million people of the Himalayan nation between India and China will be hoping that the election can bring peace and prosperity.
"We have no choice but to be hopeful," Biraj Shresthra, a 43-year-old who runs a Kathmandu electronics shop, said. "We've seen so much fighting. Maybe now it will stop."
Source: Al Jazeera and agencies