Updated at 7 p.m.

Boston Mayor Marty Walsh and public health chief Marty Martinez said Wednesday morning that the citywide positive test rate for COVID-19 has risen to 4.1 percent, just above the 4 percent threshold set for halting the schedule for a phased reopening of Boston Public Schools for in-classroom learning. That threshold was set by an agreement between the BPS and Boston Teachers Union.

Walsh said the timeline for reopening classrooms for pre-kindergarten and kindergarten students will be pushed back from Oct. 15 to Oct. 22.

But BPS will continue offering in-classroom instruction to the district’s “highest-need” students, including students with disabilities or other special needs and students who are experiencing homelessness, and who were able to opt in to in-person learning starting last week.

“The highest need students need the district … we cannot take this away from them now, or so soon after they started last week,” Walsh said. “There’s too much at stake for our young people. Every single day matters. They deserve our best efforts.”

Yet, it is not a given that teachers will show up in classrooms of high needs students. According to the agreement reached by the Boston Teachers Union and the school system last month, if the citywide COVID-19 positivity rate rises above 4 percent, “BTU bargaining unit members will have the option to be remote as well.”

BTU President Jessica Tang said in a statement Wednesday that the union will not object if special needs teachers opt to return to the classroom.

Walsh said the new changes represent a cautious response to rising rates of COVID-19, but that the city has no immediate plans to abandon in-person learning altogether.

“We’re going to look at the numbers to see where we are,” Walsh said. “If we [remain] over four percent, obviously Phase 3 and Phase 4 will have to be pushed out farther. If we’re under four percent, then we’ll be able to have a conversation about starting Phase 3, and then Phase 4.”

Asked whether there is any specific threshold at which BPS would cancel all in-classroom instruction this school year, Walsh said no, at least not now, and emphasized that all students have the option to learn remotely this school year.

Walsh was joined in announcing the changes by BPS Superintendent Brenda Cassellius, who emphasized that despite the immediate setback in the district’s phased reopening, Boston schools are safe and ready for teachers and students to return.

“It was great to see our students arrive for their first day of in-person learning in more than six months,” Cassellius said.

Schools have been sanitized and equipped with sanitation equipment and other supplies to keep students and teachers safe, Cassellius said.

“Our facilities are ready,” Cassellius said. “I’m very confident in our safety and health protocols that we put in place.”

Tang said in a statement that the decision to delay the next planned phase of in-classroom learning was the right call.

“In light of the positivity rate exceeding 4%, consistent with and in part resulting from troubling statewide and national trends in COVID-19 spread, we support the postponement of broadening in-person learning within the Boston Public Schools that the Mayor announced today,” Tang's statement said.

But Tang said the BTU remains disappointed that BPS has not adopted recommendations for this and other safety contingencies put forward by the union, including reducing the number of staff required to enter schools.

“Absent making immediate adjustments to reduce the number of non-essential staff entering school buildings, we are deeply concerned at this hour that the status quo and current approach may needlessly put thousands of staff and students in harm’s way, as we have seen multiple confirmed positive cases in the last four days,” Tang said.

The prospect of further delays to the start of school is a source of frustration for many parents. It wasn’t something Noah Sawyer, a father of two young children in Jamaica Plain, said he wanted to hear.

"I think we've been looking forward, both me and my kids, to having some more space, to back to something that resembled the routine from last year,” Sawyer said. “Y'know, it's discouraging.

Erika Sanchez, an East Boston mother, noted many working families are eager to see their children return to school because they have jobs that require them to work in person.

“Some parents are at work and they know nobody is at home to help … the kids” with homeschooling, she said. “They may have three or four kids, and they don’t have options.”

The citywide positive test rate in Boston, one of several metrics used to measure the prevalence of COVID-19 in communities, has been rising in Boston for the past few weeks, from below two percent in September.

Boston public health chief Marty Martinez said the latest numbers represent increased positive test rates in some neighborhoods, notably Hyde Park, but that rates have been flat or even fallen slightly in other neighborhoods that have seen more COVID-19 infections, including Dorchester and East Boston.

GBH News' Meg Woolhouse contributed to this report.