Updated: 09/10/12 – 11 p.m.

CHICAGO (CBS) — Mayor Rahm Emanuel said Monday he wants Chicago Public Schools officials and the Chicago Teachers Union to continue negotiating until they finish a deal to open schools again.

“Stay at the table, finish it for our children,” the mayor said.

Union teachers went on strike Monday, after failing to reach an agreement to avoid the first walkout in 25 years in Chicago.

The mayor said he was disappointed teachers decided to strike when issues of salaries and benefits have largely been settled.

“This is, in my view, a strike of choice; and it’s the wrong choice for our children. It’s not necessary,” he said. “We need to just finish the job, given all the work that’s gone in, to make sure our kids continue to get the education they need.”

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CTU Vice President Jesse Sharkey said the mayor’s assessment was “completely wrong.”

“We brought the board’s final offer to our rank-and-file bargaining committee,” he said. “We talked all the way to the end. When that committee looked at the offer, they rejected it unanimously. They said this is insufficient to keep us in school. We’re now going to keep trying to get a contract that solves all the issues, in order to go back to work.”

Sharkey said CPS administrators claim any performance success for themselves, while laying all of the blame for failures at the feet of the teachers.

CPS and CTU negotiators were back at the table Monday, working through what the mayor said are two remaining issues: a new teacher evaluation system, and hiring discretion for CPS principals. The parties quite Monday night and were expected to resume Tuesday, as the strike entered its second day.

The mayor said the two remaining unresolved issues in contract talks have come down to teacher evaluations and principals’ hiring powers.

Emanuel said he believes individual principals should have the flexibility to hire the teachers they believe are best suited for their school, not the district, and not the union.

“I don’t believe I should pick them, I don’t believe the CPS leadership should pick them, and I don’t believe the CTU leadership should pick them,” Emanuel said. “Very good teachers want to make sure there are very good teachers alongside them. That’s how schools improve their test scores, as a team, working together under the leadership of a principal who helped create that team.”

The mayor said the district holds principals accountable for the performance of their schools, so those principals should have more control over their teaching staffs.

“If we’re going to hold … our local principals in the school accountable for getting the results we need, they need to pick the best qualified,” he said. “The direction and dictation should not come out of downtown.”

The mayor insisted the teacher evaluation system at CPS has not changed in 40 years.

The union doesn’t want teacher evaluations tied to student performance on standardized tests, and claimed the new evaluation system sought by the Emanuel administration would lead to 6,000 teacher layoffs.

But the mayor said the new evaluation system was developed in cooperation with teachers, and was negotiated as part of a new state law.

“The evaluation is designed by our teachers, for our teachers, and will be revised by our teachers. It respects their understanding of their profession, and what it takes to improve the quality of the teachers,” Emanuel said.

Asked how much of the decision to strike was aimed at him, in particular, as opposed to contract disputes, Emanuel said “I don’t think that’s a good thing to do to our children.”

“That’s wrong to do. Don’t take it out the kids of the city of Chicago if you’ve got a problem with me. That’s wrong. Our kids deserve better,” he added.

He also questioned CTU’s estimates about teacher layoffs that would result from the new evaluation system.

“It’s clear – if they think 6,000 – I’m more optimistic that the teachers will pass. I have a bigger confidence in the quality of our teachers than they do, which I think is a little strange,” he said. “I don’t know how you can predict that. The teachers designed it. The teachers designed the evaluation test for themselves to take.”

The union conceded wages are not the hold-up any longer, but defended going on strike, even though the two sides are close to an agreement on salaries.

“Layoff and recall are not issues in which we’re legally entitled to strike over, but I would say, obviously those things are important for a contract,” CTU Vice President Jesse Sharkey said.