The Boston Licensing Board on Thursday approved liquor licenses for three restaurants in Dorchester, but denied requests for licenses in the South Bay Town Center mall still under construction.

Among the winners: Kriola on Hancock Street in Uphams Corner.

Board members said the restaurant met the required "public need" in part because of support from elected officials, including Mayor Marty Walsh and City Councilor Frank Baker, in part because it serves a unique market. "It's one of the few Cape Verdean restaurants in the city and also the only one in that area," board Chairwoman Christine Pulgini said.

The owners of the Lower Mills Tavern in Lower Mills got a beer and wine license fot the taqueria, named Taqueria, they want to open near the tavern on Dorchester Avenue. Board members said the public need was shown by the fact that residents approached the tavern owners with the idea of them opening a second place.

In Adams Corner, the board approved a beer and wine license for Molinari's, which serves Italian food with the pizza, citing strong support from the neighborhood.

The board, however, rejected requests for liquor licenses for a proposed Wahlburger's and AMC cineplex at South Bay Town Center, saying it was unfair to grant them licenses now when they might not be open for a year, at the earliest.

The board's decisions came on requests for the 25 licenses the board had to award this year, five unrestricted licenses that can be resold and used anywhere in the city and 20 for specific neighborhoods, including Dorchester. The state legislature gave Boston a total of 75 new licenses, to be doled out over three years, in 2014.

The licenses awarded by the board this week also need the approval of the state Alcoholic Beverages Control Commission.