LOS ANGELES (CBSLA.com) – Los Angeles Mayor Eric Garcetti and police Chief Charlie Beck Wednesday downplayed a perceived dispute between Los Angeles and New York officials over the handling of similar terror threats sent to schools in both cities. But both agreed they would like to have been kept in the loop earlier.

“The back-and-forth between New York and Los Angeles. I think it’s been way exaggerated and overplayed,” Garcetti said.

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Students went back to school on Wednesday, a day after the Los Angeles Unified School District shut down all of its campuses after receiving a terror threat that turned out to be a hoax. The last-minute school closures sent nearly 700,000 students and their parents scrambling.

Former Los Angeles police Chief Bill Bratton, who is now the New York City Police Commissioner, had accused L.A. School Superintendent Ramon Cortines of overreacting by closing the more than 900 schools.

New York City’s school district received almost the same threat. But officials there deemed it not credible and kept schools open.

Cortines said he acted out of an abundance of caution in the aftermath of terror strikes in Paris and San Bernardino. Both Garcetti and Beck expressed strong support for the decision.

But the mayor said he “would like to see greater communication, and I’d be happy to be brought in early to the decision-making process.”

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“There is no perfect scenario. It would be great if we had known that New York got the email the same time we did,” Beck said.

He said he learned about the email threat at 3 a.m. Tuesday morning. Garcetti found out about it at 4 a.m. That is six hours after LAUSD Board of Education President Steve Zimmer consulted with Chief Steven Zipperman of the Los Angeles School Police Department about what to do.

“Law enforcement really was calling the shots in terms of when to notify whom,” Zimmer said the first call was made to Deputy Chief Michael Downing, the Counter Terrorism Special Operations Bureau Chief at the LAPD.

“I immediately launched a team from Major Crimes, who’s part of the Joint Terrorism Task Force. And they started the investigation,” Downing said. That was just after 10 p.m. Monday.

Cortines, who made the decision to close all the schools, was not informed about the threat until 5 a.m. Tuesday, seven hours after the LAPD learned the news.

Zimmer said he does not think it was a mistake not to inform Cortines earlier.

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CBS2/KCAL’s Dave Lopez learned Cortines did consult with various law enforcement agencies before deciding to shut down the entire school system. But Beck would not say if Cortines specifically consulted him.