District 2 Councillor Bill Linehan said Thursday he was expecting more support than he received for his redistricting map, which passed the City Council with a 7 to 6 vote.

Linehan, who chairs the redistricting committee, also defended the map, saying it builds on past redistricting efforts. A coalition of civic groups, arguing that it violates a federal voting rights act, is vowing to file a lawsuit if Mayor Thomas Menino signs off on the map.

The City Council is required to redraw the boundaries of the nine council districts every ten years, after the release of U.S. Census figures, which detail population shifts across the city. The map moves 12 precincts in 7 council districts.

“I was using the gradual change and adjustment from past redistricting plans,” Linehan said Thursday, during a sit-down in his City Hall office.

Linehan said that based on “public discussions” and “public intentions,” that he had been hoping for nine votes in favor of his plan. But because of Open Meeting Law restrictions, he said, he could not engage in a poll.

Asked whether he had spoken to Menino about the map, Linehan said he had not, but added that he hoped the mayor would approve of it, since six out of the nine district councillors -- two-thirds -- supported his plan. City Council President Stephen Murphy, who is an at-large councillor, was the seventh vote in favor of the plan.

The other three at-large councillors – Ayanna Pressley, Felix Arroyo and John Connolly – voted against the map. They were joined by Michael Ross, Tito Jackson and Charles Yancey, who are district councillors.

Menino said Wednesday that he was reviewing the plan, but noted the high concentration of people of color in Yancey’s district, known as District 4. Members of the coalition of civic groups opposed to the plan have referred to the concentration as “packing.”

Linehan said that under his map, the district has fewer people of color than the last map. “It is a change in the right direction,” he said.

Linehan noted that District 4, made up of Dorchester and Mattapan, is also surrounded by other districts that are majority-minority: District 3, which includes Dorchester; District 5, made up of Hyde Park and parts of Mattapan; and District 7, which includes parts of Roxbury, Dorchester and the South End.

None of the maps Yancey offered would improve the situation, since Yancey wanted to unite Mattapan under one district, Linehan said.

Linehan, who would give up in the map the parts of Dorchester he represents, also pushed back on the suggestion that he added to his vote total from 2011, when he won reelection by 97 votes.

Paul McMorrow, an associate editor at Commonwealth magazine, calculates that Linehan picks up votes in the new map. And the coalition of voting rights groups notes that Linehan took out the most diverse precincts currently in his district, turning District 2 into the least diverse district in the city. Linehan presently represents parts of Dorchester, all of South Boston, Chinatown and parts of the South End.

“Because I had a close election in 2011, observers who don’t favor the outcome could construe that it was not an objective effort on my behalf,” Linehan said. But he said he was “extremely objective” as chair of the redistricting committee. “My district has changed the most,” giving up the most precincts in the process, he added.

He also picked up a precinct with 6,000 new people, he said.

Asked what he plans to do if Menino vetoes the map, Linehan said, “I’ll take it as it comes.”