Fresh off his Boston mayoral preliminary election win, Rep. Marty Walsh began the next stage of his campaign on Wednesday, shaking hands outside the Savin Hill T stop and making calls to business leaders to seek their support, including Patriots owner Robert Kraft.

Walsh was at the State House for a vote on repealing the new tech tax and to see three new members sworn in.

Colleagues cheered Walsh on the floor of the House, and Sen. Stephen Brewer of Barre flashed him a double thumbs up when they saw each other outside the building.

The veteran Dorchester lawmaker and labor union leader told reporters that he had no concerns that influential members of the Boston business community who stayed out of the preliminary election might oppose his City Hall bid now that the field has been narrowed to two candidates.

“I’m not concerned about that at all,” Walsh said, indicating he spoke directly Wednesday with Kraft, Boston Bruins owner Jeremy Jacobs, Beacon Capitol Partners CEO Alan Leventhal, real estate developer Joe Fallon and Boston Coach CEO Larry Moulter.

Walsh said not all are supporting him and most remain undecided, but Moulter has been helping his campaign. Walsh also said he planned to reach out to the 10 mayoral hopefuls who did not make the final runoff and ask for their support. Already, he said some supporters of his former foes have signed onto is campaign in neighborhoods like Charlestown where he finished in second place, but he declined to name names.

“I’m going to let them have a few days and then I’m going to be talking with them,” he said.

Walsh will face off against Boston City Councilor John Connolly in the Nov. 5 general election to succeed retiring, longtime Boston Mayor Thomas Menino. Walsh finished first in Tuesday’s preliminary election with 18.5 percent of the vote, followed by Connolly with 17.2 percent. Menino has said he will not endorse.

Walsh said the biggest difference between the two men is their political backgrounds, with him hailing from the Legislature and Connolly from the City Council.

Walsh and Connolly, both of Irish descent, now will be vying for broader support among Boston’s many communities of color after none of the six minority candidates in the field managed to break through during the preliminary.

Asked specifically about the Latino community, Walsh said he would bring a message of good jobs, improved education and affordable housing to Latino neighborhoods, specifically referencing the importance of two-way bilingual education.

Walsh also said he will focus over the next month on his plans to fight poverty, linking the problem of income disparity in Boston to other issues on his agenda.

“In order to improve schools, we have to deal with the poverty question. In order to improve economic development, we have to deal with poverty and the same with crime. We have a lot of families that worry about when their kids go out the front door if they’re going to come home. So we really have to jump into those issues and those are issues I’ve jumped in up here on Beacon Hill to work on and try to do better for my district,” Walsh said.

Though Connolly claimed the mantle of education reformer during his preliminary campaign, Walsh said his years on Beacon Hill have better prepared him to improve school performance.

“I’ve actually taken votes to reform education. I took that vote here in 2010 and I’m happy to say that we’ve turned schools around in turnaround schools. John talks about teaching for a few years in a charter school. I’ve been on the board for 17 years on a charter school,” said Walsh, who serves on the board of Neighborhood House Public Charter School in Dorchester.

Walsh said he intended to keep the debate with Connolly civil through November, in much the same way the preliminary election remained largely positive between the broad field of candidates.

“I’m not going to engage in negative campaigning. I’m going to keep it positive. I’ve never engaged in negative campaigning. I don’t believe in it. I think the people of Boston deserve better than that, and I look forward to a very good, spirited debate at some points, but a campaign that’s going to very good, above board,” Walsh said.