The second round of elections were conducted in all the 35 districts in Provinces 1, 5 and 7 yesterday and the turnout was recorded at 73.69 per cent by the Election Commission.
The local polls were earlier scheduled for two phases.
The first phase was held on May 14 in Provinces 3, 4 and 6, but the second round had to be postponed twice. A third phase has been declared on September 18 in Province 2 in a bid to placate dissenting parties, including Madhesis, by then.
"The successful implementation of the Constitution will help ensure good governance, social justice, economic prosperity and institutionalise democratic norms and culture in the society," Deuba, also the president of Nepali Congress, said in a statement.
The counting of votes begun today at 168 centres out of the 334 units where polling was held yesterday, according to Election Commission officials.
The Commission said the voter turnout in the second phase was 73.69 per cent.