Mayor Marty Walsh said Monday night he felt “confident” schools would re-open in the city on Tuesday.

Anticipating that snow would stop falling around midnight, Walsh said he did not plan to call a snow emergency, meaning the city made it through the storm without needing a parking ban, and without making it legal to secure parking spots with space-savers.

“If you put a space-saver out there, public works will come and take it,” Walsh said at an evening press conference.

Walsh also said the MBTA planned to run on a normal schedule Tuesday.

Boston was largely spared the worst of the storm as it moved out toward the Atlantic on Monday.

Still, the mayor urged residents to avoid driving if possible while crews continued to clear roadways. Five hundred vehicles were out treating and plowing roads in the city on Monday, he said.

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Meanwhile, he reminded the city of safety concerns from high winds, referencing the concerns raised by the deaths of two in Canton due to falling tree limbs.

He said the city would “monitor the situation” as cold weather was slated to hit the city later this week and into the weekend.

The city has spent $7 million of its snow budget so far this year, he said. Boston last year spent $38 million on snow costs.

Since the storm began Monday, Boston received 1,400 messages via its 311 phone service and smartphone app, Walsh said, adding that many were for information about school closures.