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Oakland Mayor Ron Dellums met with parents and students who were concerned about immigration raids at Stonehurst Elementary School in Oakland on Tuesday.

OAKLAND - Ongoing enforcement tactics by federal Immigration and Customs Enforcement personnel caused panic to erupt at several East Bay school districts Tuesday, although ICE officials said that many of the rumors that swirled among parents and school staff were false or overblown.

"This whole experience is so terrifying that it really brought out the greatest fear in everybody," said Mark Coplan, a spokesman for the Berkeley Unified School District, where the schools superintendent issued a recorded phone message to parents Tuesday promising that he "will not allow any child to be taken away from the school."

Some of the rumors "“ for example, that Berkeley middle school students were being carted off in vans "“ turned out to be false. But others "” for example, that ICE agents were conducting surveillance near an East Oakland elementary school "” were true and prompted Oakland Mayor Ron Dellums and others to rally outside the school in protest.

"We were not at a school," ICE spokeswoman Virginia Kice said. "We were at residences. There may be a situation where a residence is near to a school."

About a year after the leaders of several Bay Area cities forcefully condemned immigration raids and declared their communities to be sanctuaries for undocumented immigrants, the relationship between local officials and federal immigration authorities remains a sometimes confusing one.

Berkeley police officers were alerted, but did not participate in Tuesday morning's operation, in which ICE agents entered a South Berkeley home on Russell Street and arrested four family members who were from Mexico and living in the U.S. illegally. The arrests, involving a mother, two grandparents and an aunt of two local students, sparked a series of rumors that had concerned parents inundating the school district with calls.

"They were not people who had outstanding warrants," said Andrew McComb, director of Berkeley Organizing Congregations for Action. "They were just regular people. They picked up the grandmother in her car. She was driving down the street."

McComb said he knows the family because one member, a college student, had served as a youth organizer for his organization.

In East Oakland, Kice confirmed there was surveillance activity but said it did not lead to any arrests.

Rumors of a school raid circulated in East Oakland on Tuesday after immigration agents were spotted on E Street and on 98th Avenue, near the Stonehurst school grounds, which contains two small elementary schools -- Fred T. Korematsu Discovery Academy and Esperanza Academy.

Although the agents did not step onto the school grounds, as some believed, school staff and parent volunteers called some parents to warn them about the officers' presence in the neighborhood in case they wanted someone else to pick up their children, said Sondra Aguilera, Esperanza's principal.

When the bell rang at the end of the day, local politicians, news reporters and community activists were in abundance, but the usual flood of children was nowhere to be seen. To protect the kids "” and to make sure they were leaving with the right family members "” teachers kept the children in their classrooms until an authorized person arrived at the front office to take them home.

Alex Tinoco made sure he was at the school well before the bell rang to pick up his nephews "in case anything happened." He said the whole atmosphere was unsettling.

"The kids get scared -- they don't know what's going on," he said. "People are going to be afraid to come to school."

The schools are in the midst of spring standardized testing, but if too many children are absent today from Korematsu and Esperanza, they will have to reschedule, school officials said.

"I've already had parents say it's likely that the children are not going to come tomorrow," Aguilera said Tuesday. "I said, 'Of course you should come to school tomorrow.' I've also said, 'I understand you being afraid, but your kids will be safe on campus.' "

The Oakland school district's police force came to the campus Tuesday and will return this morning, said interim district Chief Arturo Michel.

"There won't be any (immigration) agents, I can promise you that," Michel said.

The two schools sent letters home with children informing families about the situation, and assuring them that agents did not raid the school.

In December, agents followed a pregnant mother into another East Oakland school, Melrose Bridges Academy, as she dropped off her 6-year-old daughter and then detained her for questioning.

In response to that incident, the Oakland school board passed a resolution in January that asks school staff to forward all immigration requests, including access to schools, to the district's legal department.

Staff writer Kristin Bender contributed to this report. Contact Matt O'Brien at 925-977-8463 or mattobrien@bayareanewsgroup.com.