Rep. Martin Walsh of Dorchester has shrunk his opponent’s lead in the mayoral race to within the margin of error, as Boston City Councilor John Connolly of West Roxbury edged Walsh in a recent poll, 41-39.

The numbers were closer - 35-34 - when the 503 likely voters were polled on their initial preference and not pressed to say which candidate they were leaning towards.

MassINC Polling Group found Connolly has an advantage with voters ages 18-29, voters with incomes below $25,000, parents of school-age children and people who have lived in the city for less than 10 years.

Walsh tops Connolly among voters with incomes in between $25,000 and $75,000, people who list a race other than white or black, union households and people who received some college education.

The poll commissioned by WBUR and released Wednesday has a 4.4 percent margin of error, and indicates Walsh may be closing the gap after trailing Connolly 41-34 in a Boston Herald-Suffolk University poll released Oct. 7. Walsh has steadily closed in on Connolly’s lead in subsequent polls conducted the UMass Lowell Center for Public Opinion and Sage Systems.

Walsh, who beat expectations when he topped the ticket in the preliminary election, also has a slight 42-40 edge over Connolly among voters who voted in the preliminary.

Connolly has a City Council meeting Wednesday, where Caesars Entertainment’s withdrawal from a casino bid at the Suffolk Downs track in East Boston could be a topic of discussion. Only 1 percent of voters polled thought casinos should be the “number one” issue for the next mayor, losing out to education (30 percent), jobs and the economy (22 percent) and crime (17 percent).

Walsh planned to spend some time Wednesday morning at the Alliance for Business Leadership in the Back Bay. Both candidates will be in Roxbury Wednesday evening for a “Communities of Color” debate.

The two debated at WGBH Tuesday night, a forum where Connolly questioned whether Walsh could persuade unions in contract negotiations, as the former top union official’s calls for an end to third-party attack ads on Connolly went unheeded. Walsh said he was “very upset” about a flyer criticizing Connolly and said “I’ve told the people doing this to stop doing it.”

Connolly said the exchange threw into question whether Walsh could, as he has professed, handle labor negotiations better because of his time as a union official.

“They’re not listening to you now. How do we know they’ll listen to you when you’re actually mayor?” Connolly asked.

Walsh, meanwhile, has outrun Connolly in wrapping up endorsements from elected officials and former opponents, securing the support of former mayoral candidates John Barros, Charlotte Golar Richie and City Councilor Felix Arroyo, as well as Congressman Michael Capuano, a Somerville Democrat who represents most of Boston.