CHICAGO -- Negotiations were scheduled to continue on Tuesday between Chicago Public Schools officials and the city's teachers' union as 350,000 students stayed out of classes for a second day during Chicago's first teachers' strike in 25 years.

Labor negotiations over a new contract for the teachers dragged on into Monday evening, but again proved unfruitful, even as political pressure mounted on Mayor Rahm Emanuel, whose education policies are at the heart of the union's complaints.

"I believe it was unnecessary," David J. Vitale, president of the Chicago Board of Education, said about the strike as he left the building where talks were still taking place Monday night. "It was avoidable, and we need to get this over with and get our kids back to school."

Still, Mr. Vitale expressed optimism that an agreement was within reach, and school officials have said the only unresolved issues are how to evaluate teachers and whether teaching openings should automatically go to laid-off teachers. They say they have made significant concessions in contract talks, including what would amount to a 16 percent pay increase for teachers over four years.

But union leaders say there continues to be an array of differences, including benefits, raises based on experience level, the lack of air-conditioning in classrooms and training days for teachers. The school system faces what is projected to be a $1 billion deficit in the system's operating budget next year.

Labor groups and teachers in other cities voiced support for strikers here, suggesting that the fight in Chicago was merely one glimpse at a mounting national struggle over unionized teachers' pay, conditions, benefits and standing.

The strike, the first in a major city in a half-dozen years, has also laid bare the rift between unions and Mr. Emanuel, a Democrat and former chief of staff to President Obama, raising the prospect that a lingering strike in the president's hometown might become an issue in a presidential election year when Democrats are depending on the backing of labor.

"You have a situation where the teachers feel totally and completely disrespected," said Randi Weingarten, president of the American Federation of Teachers, the parent union of the striking teachers. In this case, Ms. Weingarten said she blamed Mr. Emanuel for an aggressive push to extend the length of the school day and for a promised raise that was later rescinded. "He created the seeds of a lot of frustration and mistrust," she said.

For his part, Mr. Emanuel, facing the most serious crisis since he became mayor in 2011, deemed the work stoppage an avoidable "strike of choice," urged teachers to return to work and seemed eager to dismiss all talk about political fallout -- for himself or for Mr. Obama, whose former aides founded a "super PAC" that Mr. Emanuel had, until he suspended his work with it on Monday, said he would assist until Election Day.

"Don't worry about the test of my leadership," Mr. Emanuel said, in an appearance at one of scores of sites opened in a rush as part of a contingency plan to manage displaced students who had nowhere else to go. "Don't take it out on the kids of the city of Chicago if you have a problem with me."

Republicans were quick to weigh in on the circumstances that had pitted a Democratic mayor against 26,000 unionized teachers. Mitt Romney, the Republican nominee for president, issued a statement expressing disappointment in the teachers here, adding, "Teachers' unions have too often made plain that their interests conflict with those of our children, and today we are seeing one of the clearest examples yet." And Pat Brady, the chairman of the Illinois Republican Party, had called on Mr. Emanuel to set aside political fund-raising to focus on the schools crisis.

Mr. Obama on Monday issued no specific reaction to the strike. Jay Carney, the White House press secretary, said: "His principal concern is for the students and families who are affected by the situation. And we hope that both sides are able to come together to settle this quickly and in the best interest of Chicago's students."

For months, a conflict had been simmering here between the teachers and Mr. Emanuel, who has pledged to make the most comprehensive changes in the Chicago Public Schools in a decade. Still, the strike, announced around 10 p.m. on Sunday, took many by surprise.

On picket lines outside the schools here, teachers said they were troubled by a new evaluation system and its reliance on student test scores. Teachers spoke of rising class sizes, much-needed social workers, slow-to-arrive reference books, and, again and again, a sense of disrespect.

Teachers also clearly saw the strike as a protest not just of the union negotiations in Chicago but on data-driven education changes nationwide, which many perceived as being pushed by corporate interests and relying too heavily on standardized tests to measure student progress.

At Lane Tech College Prep, where many passing motorists honked their support for the teachers, Steve Parsons, a teacher, said he believed the city was ultimately aiming to privatize education through charter schools and computer programs that teach classes online.

"We need to stay out as long as it takes to get a fair contract and protect our schools," he said.

Around Chicago, parents said they were struggling to find places to send their children for some uncertain number of days or weeks or, as one worried parent offered unhappily, months. Some brought children to their workplaces, and others took days off. City officials opened 144 schools for half-days of games, movies, puzzles, basketball and meals with nonunion workers, but some parents expressed concern about the safety or value of those options, and others seemed uncomfortable with the prospect of crossing picket lines to enter.

"This was very bad timing," said Karen Miles, who said she had to cancel work meetings on Monday to juggle her daughters. "I plan my day around their school," she said, inside her daughters' school -- one of the contingency sites -- on the city's North Side, where one sign read, "Your kids deserve what Rahm's kids get," an allusion to the mayor's children's attendance at a private school.

"I don't get paid," Ms. Miles added, "if I don't work."

In recent years, school strikes in major cities have been relatively rare, last occurring in Detroit in 2006.

By late Monday, thousands of teachers and supporters, including a sprinkling of firefighters and Teamsters, packed a rally downtown, wrapping around two blocks and, at points, completely blocking traffic. The mood was festive, marked by drums and loud shouts of "Hey, hey, ho, ho, Rahm Emanuel's got to go!"

Kelly Farrell, a kindergarten teacher at Higgins Elementary on the city's South Side, said her class had so many pupils that she did not even have enough seats for them all. "They are 5 years old," she said. "They want their teacher's attention, and there is one of me and 43 of them."

Reporting was contributed by Motoko Rich and Idalmy Carrera from Chicago, Steven Greenhouse, Jack Begg and Colin Moynihan from New York, and Peter Baker from Washington.

First Published: September 11, 2012, 5:00 p.m.