The applicants clustered on Kissena Boulevard, clutching documents from around the world, trading familiar stories with strangers in a driving rain outside the Queens Library in Flushing. There were the police encounters, the school visits, the fraught hospital trips — all negotiated without the bureaucratic lubricant of local identification.

“We feel naked,” said Mauricio Peña, 34, who is originally from Honduras. “We feel like we don’t exist.”

At his side, a peer, who immigrated from Malaysia 17 years ago, nodded beneath his umbrella.

Such was the scene at enrollment sites across New York City on Monday, with crowds gathering by the hundreds as the de Blasio administration introduced the country’s largest municipal identification program.

The card is intended to help immigrants, undocumented or otherwise; homeless people; and others who struggle to navigate city services and institutions. Officials have also sought to entice New Yorkers with a package of benefits for those who enroll this year: prescription drug discounts, free memberships for a year to zoos, museums and other city institutions, and library access, among other perks.