A small bomb also went off outside a hospital in the centre of the capital Kathmandu on Thursday but caused no injuries.
The head of the United Nations mission in Nepal said he was "deeply shocked" by the deaths.
"Security personnel against whom there is reasonable suspicion of excessive use of force or political partiality should be suspended while there is an investigation independent of their chain-of-command," Ian Martin said in a statement.
The centrepiece of a 2006 peace deal with Maoist rebels, Thursday's elections will produce an assembly meant to write a new constitution, ditch a 240-year-old monarchy and turn the Himalayan nation into a republic.
But analysts and diplomats say the violence during the run-up to the vote could undermine the credibility of Nepal's first national polls since 1999.
Maoists said a candidate from the rival Nepali Congress party ordered police to fire on their cadres in western Nepal late on Tuesday, killing six on the spot. Another died later in hospital.
"This is thuggery and the guilty should be punished," said senior Maoist leader Baburam Bhattarai.
Home Ministry spokesman Modraj Dotel said the incident was being investigated and anyone found guilty would be punished.
A candidate from the Communist UML party was also killed in another incident in nearby Surkhet district, Dotel said.
On Wednesday Maoist and UML activists staged a protest about that death. Maoists said police fired on that protest, killing another of their cadres.
The latest deaths take to at least 12 the number of people killed in election-related violence so far.
The United Nations, monitoring the elections and peace process, say the former rebels are guilty of intimidating voters and preventing campaigning in some of their former strongholds.
But the UN has also accused other parties of violence and using state machinery to influence voters.
Nepal has deployed at least 135,000 police to provide security during the vote.
Hundreds of international monitors, from organisations including the United Nations, European Union and the Atlanta-based Carter Centre are monitoring the vote.
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