The two sides have been in a dispute over wages, health premiums and pensions since the contract expired in August.
The strike comes at a sensitive time for the archdiocese, with Pope Benedict XVI set to visit New York later this week on his first-ever trip to the United States as pope.
Kielkucki said the strike was not timed to coincide with the pope's visit, but some parents couldn't help but note the timing.
"I thinks it's the right time with the pope being here to show more notice to their needs, and I hope it works for them, and I hope they get what they need," said Jamie Longo, who was picking up her child at Maria Regina High School in Hartsdale, one of the schools that closed early.
Archdiocese spokesman Joe Zwilling said nearly all the teachers at three high schools reported to work; four others closed early; and early dismissals were planned at the remainder.
A second lay teachers' union, the Federation of Catholic Teachers, which represents 3,000 teachers at 206 schools, accepted a four-year contact from the archdiocese last week.
Under the terms of that contract, teachers will get a 3 percent raise in the first year and 4 percent in each of the other three years. Teachers also will contribute 10 percent to their health insurance plan. Previously, they paid anywhere from 5.9 percent to 7.6 percent.
Zwilling said the terms the archdiocese offered to the smaller union were similar.
"We have made an offer to the union that preserves the first three years of the contract offered in November, but adds a fourth year that gives the teachers what they had identified as their top priority and gives the archdiocese what we identified as our top priority," he said.
"For the union that was $60,000 top salary. For the archdiocese it was teachers contributing the same 10 percent to their health insurance premiums that other lay employees pay."
The New York archdiocese includes schools in Manhattan, Staten Island, the Bronx and several counties north of the city.
Four schools closed early Tuesday: Our Lady of Lourdes High School in Poughkeepsie; Maria Regina; and Cardinal Spellman and Cardinal Hayes high schools, both in the Bronx.
The other schools affected by the strike were Monsignor Farrell and Moore high schools, both on Staten Island; Cathedral High School in Manhattan; Archbishop Stepinac High School in White Plains; John F. Kennedy Catholic High School in Somers; and John S. Burke Catholic High School in Goshen.
Strife between the archdiocese and the two teachers' unions has grown in recent weeks.
Catholic school students were once taught largely by nuns and priests, who essentially worked for free.
But the number of lay teachers has surged in the last two decades, and they now make up about 85 percent of the faculty at the New York archdiocese's 216 schools, according to Kielkucki.
The Catholic school teachers earn an average of $45,000 a year, about 30 percent less than their public-school colleagues.
Outside Maria Regina, about two dozen teachers picketed as parents arrived to pick up their children.
"We didn't become teachers to stand on a strike line but we're doing what we need to do in order to get a fair contract," said teacher Jill Michael.
Michael said the strike had nothing to do with the pope's visit. "We just want this contract settled," she said.
Lisa Luglio was among the parents expressing support for the teachers.
"I think they should be totally compensated for what they do. They go way out for the kids," she said. "These are good teachers."
For more on the teachers strike, and which schools are closing early, Click Here.