NEW YORK — Hundreds of suspicious packages in Midtown Manhattan were reported to the Police Department this year, but its response to one discovered at Trump Tower on Tuesday underscored the challenges and headaches that come with protecting the home of the president-elect.

Though President-elect Donald Trump was in Florida during the scare, the package — an abandoned backpack filled with toys — set off an evacuation that sent visitors and employees at the tower running into the streets about 4:30 p.m. and snarled traffic around the Fifth Avenue building.

The police blocked off some of New York City’s most glutted arteries at the peak of the holiday season rush hour. The closing lasted just over an hour, but it choked traffic for miles. City buses were diverted, hordes of pedestrians were crammed behind barricades and stores in the area were forced to close.

“The current heightened security awareness in this area clearly drew much more attention to yesterday’s incident,’’ Stephen Davis, a spokesman for the Police Department, said Wednesday. “This was not a threat or even a mock device but rather an apparent case of a child’s backpack being left inadvertently near the building.’’

In Washington, suspicious packages near the White House have become largely routine, and are rarely disruptive. The 1600 section of Pennsylvania Avenue has been closed to vehicle traffic since 1995.

At Trump Tower, the backpack was found by the Secret Service by the lobby entrance of the Niketown store, where a corridor leads into a public atrium, the authorities said.

A rough cordon around the 58-story tower, which is between 56th and 57th Streets, and its surroundings went into almost immediate play: Both Fifth and Madison Avenues were closed to traffic from 55th to 57th Streets.

A growing number of stores are unhappy about how the protection efforts, including permanent street closings and police patrols, have hurt business around the tower.