The crowded poll is expected to see the former political party of ousted strongman Suharto win the most votes, but not a majority.
Police said an unidentified group of about 20 men, armed with knives, arrows and machetes, ambushed the policeman and election official as they were delivering election equipment to the southeastern district of Okaba on Saturday.
An executive of the Papua election commission, Frits Ramandey, told Detikcom online news service both victims had died in the attack.
Meanwhile, polling stations opened in stages across the world's most populous Muslim nation amid tight security in what is billed as the biggest one-day vote in history, and is only Indonesia's second democratic election since Suharto's fall in 1998.
The 82-year-old former autocrat was one of the early voters, casting his ballot in an elite Jakarta neighbourhood.
A win for Golkar, which has sought to distance itself from Suharto, could badly dent President Megawati Sukarnoputri's chances of winning a second term in Indonesia's first direct presidential election on 5 July.
"The economy has suffered, the economic recovery has not yet finished. And you know the increasing of unemployment, the poverty. The prices are high. That is why the people are not happy"
Golkar presidential candidate
"The economy has suffered, the economic recovery has not yet finished. And you know the increasing of unemployment, the poverty. The prices are high. That is why the people are not happy," said Golkar presidential candidate Akbar Tandjung as he cast his vote near his home in Jakarta.
"They know Golkar were already in power for 32 years. They know Golkar has the experience. That is why I think they would like Golkar in power again."
Monday's results will be followed by a scramble to build coalitions before the presidential election. Recent opinion polls showed Megawati had lost her status as frontrunner.
Amid fears of unrest during Monday's vote, National Police Chief General Da'i Bachtiar said 275,000 police had been deployed around the country.
Former president Suharto was
one of the early voters
The ballot will also test the popularity of conservative Islamist parties in the wake of bomb attacks by people linked to Usama bin Ladin's al-Qaida network.
The military were on alert in separatist hotspots such as Papua and Aceh.
Polling booths in eastern Indonesia were the first to open, although an hour after the scheduled time. The region includes Papua, about 3000km east of Jakarta, where independence demands have simmered for decades.
Thousands of polling stations
Dozens of mostly illiterate Asolokabal villagers sat in the blazing sun south of the town of Waimena in Papua and watched officials give voting demonstrations.
In Jayapura, the provincial capital, some stations were unable to open after authorities failed to deliver ballot papers and boxes, witnesses said.
There are nearly 600,000 polling stations across the country.
There are nearly 600,000 polling
stations across the archipelago
In Jakarta early voters queued outside polling stations. Streets in the normally bustling capital were empty and quiet, with a national holiday declared.
Suharto who has featured in advertising for a party run by his daughter, was accompanied by dozens of supporters as he strolled, unaided except for a walking stick, to a polling booth near his home in Jakarta's Menteng area.
His lawyers say he is too sick to face trial on corruption charges.
Polls officially close at 06:00 GMT on Monday. First results are not expected to be announced until 11:00 GMT. But given the size of Indonesia, it may take a day or two before a significant number of votes have been counted.
More than 147 million voters are eligible to participate in elections for the 550-seat parliament and local legislatures. A total of 7800 candidates from 24 parties are competing for seats in the national parliament.
Megawati's Indonesia Democratic Party-Struggle (PDI-P) won 34% of the last poll in 1999, the highest of any party.
Golkar won 22.5%. Both are secular nationalist parties.
Golkar has tapped a yearning for the stability and rapid economic growth of Suharto's rule. But little separates it from most of its rivals in terms of policy.
Besides putting Golkar in advance of Megawati's party, recent opinion polls show her trailing for the first time in the presidential election race behind former chief security minister Susilo Bambang Yudhoyono.
The retired general is the candidate of a smaller party and had quit Megawati's cabinet last month after a row with her.