Authorities recorded a 70.5 per cent voter turnout, slightly lower than the 71 per cent recorded in the first phase on May 14.
The elections were largely held in a peaceful and fair manner in all the polling centres, despite some sporadic incidents at a few places, Chief Election Commissioner Ayodhee Prasad Yadav said.
The counting of votes will start as soon as the ballot boxes reach the counting centres, he said.
The voting began at 7 AM in a total of 8,364 polling centres and concluded at 5 PM.
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Voting in two polling centres in Bajhang district were halted due to clashes between the cadres of Nepali Congress and Communist Party of Nepal (Unified Marxist-Leninist), according to the EC.
In ward number 9 of Rolpa Municipality, thevoting was halted after a voter poured acid into a ballot box.
According to police, the acid destroyed 10 ballot papers. Deputy Superintendent of Police Ram Prasad Gharti Magar said they were investigating the case.
He said the local villagers were excited to participate as the second phase of local-level elections were held in peaceful, free and fair manner.
Deuba assured that the Constitution's full-fledged implementation would take its course once the local government was established, and that the development works would move forward efficiently, rapidly and transparently.
In a brief statement, Deuba said the elections were held so that the villages' governments are established by the villagers themselves.
Meanwhile, Nepal media reported that at least four persons died, apparently due to natural causes, while casting their votes.
Though the local polls were earlier scheduled for two phases, the second phase had to be postponed twice -- and a third phase had to be declared -- in a bid to accommodate the dissenting parties, including the Madhesis, that are yet to commit to the polls to be held in Province 2 on September 18.
In the first round of polls held on May 14 in Provinces 3, 4 and 6, voter turn out was recorded at 71 per cent.
The Nepal government had earlier this month postponed the date of elections in the disputed Madhesi-stronghold Province 2 by nearly three months, adding a third phase in the polls that will take place in September.
The Rastriya Janta Party Nepal, the key Madhesi party, have fielded their candidates as independents in the election.
The Election Commission said 62,408 candidates were contesting the second phase of elections.
Votes were cast secretly under the first-past-the-post electoral system on the basis of one post, one vote pattern.
The Ministry of Home Affairs said yesterday that the government had made fool-proof security arrangements to ensure that the second phase of local level elections took place in a free, fair and peaceful environment.