Nasim, also the health minister, shrugged off allegations of irregularities in the Apr 28 polls.
“We drew lessons from our losses in the last city polls, corrected them and secured victory in [Tuesday’s] elections,” he told reporters in Dhaka on Saturday.
The BNP, which sat out the 2014 general elections, endorsed candidates for the city polls.
But it boycotted the elections midway raising allegations of rigging.
Awami League-endorsed candidates Annisul Huq, Sayeed Khokon and AJM Nasir won in Dhaka North, South and Chittagong respectively.
BNP-backed candidates had won mayor’s post in Rajshahi, Khulna, Sylhet, Barisal and Gazipur city corporations during the Awami League’s last term.
Nasim claimed the BNP pulled out of the elections midway to create a controversy with defeat staring them in the face.
“They tried to prove that free and fair elections are not possible under [Prime Minister] Sheikh Hasina but failed,” he said.
The ruling party presidium member admitted that there were “one or two stray incidents”.
“But there was no large-scale irregularities in this election,” he added.