Mayor Thomas Menino has vetoed a second redistricting map sent to his desk by the City Council on a 7-6 vote, again giving as his reason an over-concentration of people of color in District 4.

Councillor Tito Jackson had mounted a surprise push for the second map, which redraws the boundaries of district council seats, at last Wednesday’s City Council meeting, after Menino had vetoed an earlier map, which was backed by Councillor Bill Linehan, the chair of the council’s redistricting committee.

“My concern about the last plan was that it concentrated ‘our many citizens of color into too few districts, and in doing so may limit their equal opportunity to elect candidates of their choice,’ ” Menino wrote in his veto message on Monday, quoting from his veto letter of Sept. 6. “This overconcentration was especially true in District 4, and the second map you passed shares the very same problem there and almost the very same figures.”

Menino noted that in both maps 70 percent of District 4’s voting age population is black and 95 percent is non-white. “In a city where diversity is found broadly, I had asked that you endeavor to avoid over-concentration of minority voters, and I make that same request again.”

A redistricting committee meeting is scheduled for tomorrow (Friday) at 11 a.m. in City Hall, and the Coalition of Color, which has pressed for vetoes of the two maps, has been invited to state their case, according to Linehan’s office.

“It’s about how these districts represent the people, the demographics of Boston,” Menino told the Reporter after an event at the Dever-McCormack School. “The changes that will be made will not destroy anybody’s political career.”

Menino reiterated that point when the topic of redistricting came up during a neighborhood meeting in Bowdoin-Geneva, saying the map he vetoed took care of “individual interests, not the city’s interests.”

In a statement released through an aide, Linehan said he was not surprised by Menino’s veto. “Based on this veto, the mayor indicates we all have some work to do,” Linehan said.

In its latest call for a veto, the collection of civic and voting rights groups known as the Coalition of Color had also demanded the removal of Linehan as redistricting committee chair.

The council, which must redraw the maps to account for population shifts revealed by US Census figures, is facing a November deadline since a map must be approved a year before the 2013 election.

District 3 Councillor Frank Baker voted in favor of the map crafted by Councillors Jackson and Matt O’Malley. With councillors returning to the drawing board, Baker said, “I’m concerned about Dorchester being split.”

In last week’s surprise vote, councillors for the Jackson-O’Malley map, aside from Jackson and O’Malley, included Councillors At-Large Connolly, Felix Arroyo, and Ayanna Pressley. Baker and District 8 Councillor Michael Ross joined the majority.

Linehan, Council President Stephen Murphy, and several district councillors voted against the map. Linehan said the Jackson-O’Malley map, which moved around fewer precincts than his map, was essentially the same as his map.

“It’s almost exactly the same,” he said.

But the votes between his map and the Jackson-O’Malley were almost inverted. And Arroyo noted in a floor speech that the voting rights groups, which had threatened to sue if the Linehan map had passed into law, had also sent signals months ago that the Jackson-O’Malley map was more palatable.

Both maps placed the Polish Triangle into District 3 and put the precinct surrounding City Hall into District 2 instead of District 1.

Charles Yancey, the District 4 councillor, voted against the Jackson-O’Malley map, saying it did not unite Mattapan. He had also voted against Linehan’s map, citing the same reason.