Amidst a surge of anti-Semitic attacks, City Hall announced Thursday it is reopening a city program that covers security costs for yeshivas and other religious schools.

The move by Mayor de Blasio will allow the institutions to apply to the city’s $20 million fund until January 17, even if the institutions missed the initial June deadline.

So far, City Hall awarded $14 million, leaving $6 million available for this new round of applicants — potentially enough for 70 schools, officials said.

But two city councilmen told The Post that de Blasio’s move doesn’t go far enough.

They want City Hall to change the program’s criteria so yeshivas with fewer than 300 students can qualify for the assistance.

“That seems to be a logical thing to fix,” said Councilman Mark Levine (D-Manhattan), who is pushing for the change alongside Brooklyn’s Chaim Deutsch.

The size requirement means that several smaller yeshivas along Manhattan’s West Side have been left vulnerable, Levine argued.

Deutsch (D-Brooklyn) has introduced a bill that would expand the program to include smaller schools and cultural institutions.

“We’ll review the legislation and look forward to working with the sponsors,” said de Blasio press secretary Freddi Goldstein.

A spokeswoman for City Council Speaker Corey Johnson said the bill was “going through the legislative process.”

Deutsch is also pushing for a measure that would allow synagogues to get gun permits for security more easily.

The moves came as Hizzoner met Thursday with Jewish leaders in Borough Park for two hours in an attempt to calm fears in the city’s Orthodox neighborhoods and criticism about the city’s sluggish response.

There were at least a dozen anti-Semitic incidents in the city in the past week following the deadly December shooting at a kosher market in New Jersey and the machete attack on a Hanukkah celebration in Monsey, NY on Saturday.

“There’s a real sense of deep, deep fear that anti-Semitism is growing that it’s taking on a more violent form here and all over the country,” the mayor told the press after the closed-door meeting.

“That’s what the conversation is about, how do we stop that,” he said.

But not everyone was invited. Councilman Kalman Yeger — who represents nearby portions of Borough Park and has repeatedly clashed with de Blasio — was left out.

Yeger is demanding de Blasio put more cops in the city’s Jewish neighborhoods.

“We’re seeing attacks every single day, so how can we say that what’s been done is sufficient?” Yeger asked The Post.

A mayoral spokeswoman defended Yeger’s exclusion by saying the sitdown was set up for local religious leaders and advocates — not elected officials.

“This was an operational meeting to hear how we can better support the community through agencies the mayor controls,” the person said.

Despite the skirmish, de Blasio sided with Yeger and pledged to the Jewish leaders at the meeting that the NYPD would further step up its presence in response to the string of recent attacks.

“The leaders were right in saying they wanted to see more and I agree with them and we will produce it for them,” he told reporters after the meeting.

Rabbi David Niederman, executive director of the United Jewish Organizations of Williamsburg, Inc., welcomed the move.

“The mayor is adding more people to the locations that are under siege. He understands that it’s different than it was before. It used to be our communities were safe; but, unfortunately, it’s worse,” Niederman said.