Striking school bus drivers and private bus companies concluded their meeting with a mediator on Monday with no resolution to the ongoing school bus strike, now entering its third week, and no plans for another meeting.

While the mediator expressed confidence that progress was made, the head of Local 1181 of the Amalgamated Transit Union, reiterated what he said last week: he wants to talk to the mayor.

“While this meeting was a step in the right direction, we continue to believe that Mayor Bloomberg has a responsibility to take part in these discussions and join us at the table,” said Michael Cordiello in a statement. “Despite what the Mayor and his Administration have said, his involvement in the process is not only completely legal, but is necessary to move towards a resolution and end this strike.”

The mayor gave the union leaders and representatives of the bus companies a place to meet — Gracie Mansion — as well as a mediator, Justice Milton Mollen, who was involved with the last bus strike in 1979. But he did not send anyone from City hall to the talks because he has argued this is a matter between privately run companies and their workers’ union, not the city.

But ATU members said they are striking because of the city’s decision to put out requests for new bids for school bus routes, without longstanding job protections for current drivers. Without seniority protections, union leaders say, they won’t return to work.

“We are behind the union president 100 percent. We’re not even asking for sick days, which is something that would be normal. We’re just asking for job security,” said Reina Martinez who has been a bus driver for about 26 years. A Queens resident, Martinez gets to pick her “runs” because she has seniority.

Without those seniority protections, known as Employee Protection Provisions, or EPPs, she believes she will lose her job.

“If we go back to work without that EPP, we will go back, but we will lose our jobs two months from now. So what difference does it make? We might as well fight for it,” she said.

The New York Times described the seniority perks, and the system of picking runs in this article.

Meanwhile, the latest attendance figures from the Department of Education remained average for the citywide student population, at 91.3 percent, but about 20 percentage points lower for the special education students in District 75 schools. Attendance rate for them was 67.5 percent.

Also on Monday, attorneys for Local 1181′s pension fund sent a letter to Chancellor Dennis Walcott warning that the D.O.E. will be on the hook for pension withdrawals, if it eliminates the Employee Protection Provisions and new contracts are signed with bus companies that don’t pay into the fund.