Amid growing calls for the MBTA to suspend July 1 fare increases in the wake of a disruptive Red Line derailment, T officials appear poised to begin collecting additional money from riders.

Boston Mayor Marty Walsh publicly called Monday for the MBTA not to raise prices on July 1 as scheduled "until the Red Line is fixed" following last week's derailment near the JFK/UMass station. An online petition with a similar proposal has drawn more than 5,000 signatures.

However, during a Monday meeting of the T's oversight board, both Chairman Joseph Aiello and Transportation Secretary Stephanie Pollack expressed skepticism about pausing the fare increases, which vary by ticket type but average about 5.8 percent.

General Manager Steve Poftak similarly described the idea as infeasible last week. "The fare increase will occur on July 1," he said Friday during a press conference at the derailment site.

"Changing the fare increase that's already put into effect is not the correct gesture," Pollack said Monday.

An across-the-board freeze would cut into roughly $30 million that the MBTA is counting on for next year's budget, Aiello and Pollack said, and allowing free rides on just the Red Line could increase crowds during an already-strained period.

"I personally have great empathy for trying to figure out how to mitigate the terrible experiences that folks had last week and the subpar service they are likely to receive over the next couple of weeks," Aiello said. "The broader fare increase, I think, is too much of a blunt instrument to roll back at this point, given that we use a lot of those resources to fund maintenance."

During the meeting, Braintree Mayor Joseph Sullivan — who is also a member of the state transportation board — asked other officials what they could do to meet the public's requests for relief. He suggested the board could ask the Legislature to cover any revenue lost by pausing fare increases to allow for a freeze without affecting the MBTA's financial outlook.

Sullivan later told reporters he does not believe suspending fare increases across the system is viable, but he does want to see some compromise made. One option, he said, could be to offer "a few days" of free rides on the Red Line.

"What is happening is a loss of confidence, a question of safety, from this derailment," Sullivan said. "I'm hopeful we can come up with some type of recognition, some type of solution, to offset this fare increase that is coming."