CHICAGO — Negotiators were back behind closed doors Tuesday on the second day of Chicago’s teachers strike, but publicly the teachers union and school board could not even agree on whether they were close to a deal.

The union issued a statement at midday saying negotiators had returned to the bargaining table and were discussing one of the most serious remaining issues, a new teacher evaluation system. But the union said it had signed off on only six of 48 articles in the contract and that the two sides had ‘‘a considerable way to go.’’

‘‘To say that this contract will be settled today is lunacy,’’ union president Karen Lewis said at one of several sites around the city where teachers gathered to chant and wave placards.

School board officials have repeatedly described the two sides as being close and suggested bargaining could be wrapped up quickly with agreements on the evaluations and a dispute about the recall of teachers who lose their jobs.

Earlier, Mayor Rahm Emanuel reiterated his belief that the strike could have been avoided altogether.

At an appearance with principals and former principals, he addressed another sticking point over how teachers are hired, insisting that principals — not the city or the union — should have full control to pick their team.

‘‘I don’t think downtown should be in the business of selecting teachers that the local school principal should select if you’re going to hold them accountable,’’ Emanuel said, as several hundred protesting teachers chanted and banged on drums.

A group of seven educators backed him up. One was Mahalia Hines, a member of the Board of Education and a former principal at a school in Englewood, a neighborhood beset by violence. She said it was essential that she be allowed to choose her staff ‘‘in that war zone.’’

Meanwhile, parents and caregivers were once again scrambling to figure out what to do with more than 350,000 idle children. On Monday, only about 18,000 students showed up at schools and other venues where authorities organized activities and provided meals for those in need. That means the vast majority of parents have to make alternative arrangements or leave their children unsupervised through the day.

In a year when labor unions have been losing ground nationwide, the walkout’s implications were sure to extend far beyond Chicago, particularly for districts engaged in similar debates.

‘‘This is a long-term battle that everyone’s going to watch,’’ said Eric Hanuskek, a senior fellow in education at the Hoover Institution of Stanford University. ‘‘Other teachers unions in the United States are wondering if they should follow suit.’’

The union had vowed to strike Monday if there was no agreement on a new contract, even though the district offered a 16 percent raise over four years and the two sides had essentially agreed on a longer school day.