As the city kicks off year two of its universal pre-kindergarten initiative, the official at the head of the push defended the city’s new policy to allow religious providers to include prayer breaks during the school day.

“We’ve always had religious providers as part of the system. What we do is make sure that we have a strict separation, of course, of church and state,” Deputy Mayor Richard Buery said Tuesday on WNYC’s Brian Lehrer Show. “Public dollars can only be used for secular instruction, but providers are allowed to – they’ve always been allowed to – have instruction outside of the hours that the public pays for and that’s been true for 20 years, perfectly consistent with the Constitution.”

The city requires full-day pre-K providers to offer 6 hours and 20 minutes of secular instruction, five days per week. Last year, officials told participating religious schools that any religious activities or instruction would have to take place before or after the school day — concerning leaders of many Jewish yeshivas, who said the rules would make school days uncomfortably long for four-year-olds. Many of those schools opted not to participate in the program last fall.

But as the city looks to add an additional 17,000 seats by September, the city has now told providers they can now have one short break for “nonprogram activities” during the school day, spread instruction over six days, and operate on federal holidays to meet the required 180 days of instruction per year, according to the Jewish newspaper Hamodia. That has prompted criticism from civil liberties groups, with NYCLU Executive Director Donna Lieberman telling the Associated Press this week that the prayer break is “an end run around the separation of church and state.”

On Tuesday, Buery said “there are very clear opt-out rules” from religious instruction and noted that providers are obligated to provide children that do not want to participate with “high-quality, enriching activities during that break.”

All of the city’s full-day pre-K providers must give the same amount of non-religious instruction per week and pass the same quality review, he said, while the new flexibility ensures that “high-quality providers can be a part of the system.”

The city has approved an additional 200 programs to offer full-day pre-K next year, including charter schools, district schools, religious schools, and nonprofit organizations, Buery said. The city’s goal is to provide seats for 70,000 city four-year-olds by September, with a seat available for every child whose family wants one.

The application process for pre-K programs launched Monday, and Mayor Bill de Blasio said nearly 22,000 families submitted applications in the first 24 hours. The deadline for fall enrollment is April 24.