VATICAN CITY (RNS) Leaders of an umbrella group that represents the majority of U.S. nuns met with top Vatican doctrinal officials on Tuesday (June 12) in an atmosphere of “openness and cordiality,” according to a Vatican statement.

Still, the Vatican made clear that the Leadership Conference of Women Religious -- which represents most of America's 57,000 nuns -- "remains under the supreme direction of the Holy See" and appeared to offer little wiggle room in its crackdown on the nuns' leaders.

The meeting was called after the Vatican's doctrinal watchdog office, the Congregation for the Doctrine of the Faith, issued a "doctrinal assessment" this spring that criticized the LCWR for not speaking out strongly enough against gay marriage, women priests and abortion.

The Vatican also chided the women for “serious doctrinal problems” among many LCWR members, and said LCWR conferences suffered from “a prevalence of certain radical feminist themes incompatible with the Catholic faith.”

The LCWR's president, Sister Pat Farrell, and executive director, Sister Janet Mock, met with American Cardinal William J. Levada, who heads the CDF, and Seattle Archbishop Peter J. Sartain, who has been appointed by the Vatican to oversee a top-to-bottom reform of LCWR.

The meeting, following a move by the Vatican that has opened a large divide between the nuns and laity on one side and the hierarchy on the other, was notable for its muted tone and lack of specifics.

“We are grateful for the opportunity for open dialogue and now we will return to our members to see the next steps,” Farrell told reporters after the meeting.

According to an official statement by Vatican spokesman Rev. Federico Lombardi, “the meeting provided the opportunity for the Congregation and the LCWR officers to discuss the issues and concerns raised by the doctrinal assessment in an atmosphere of openness and cordiality.”

In its statement, the Vatican made clear that the LCWR “is constituted by and remains under the supreme direction of the Holy See.” In that context, the “doctrinal assessment” is meant to “assist” the sisters in “promoting a vision of ecclesial communion” founded on the “teachings of the Church as faithfully taught through the ages under the guidance of the Magisterium.”

LCWR said in a statement that it will “determine its course of action in response" to the Vatican crackdown at its annual assembly in August.

The nuns' group has received widespread support in the United States, both inside and outside the Catholic Church, with lay vigils in support and even an appearance by a prominent nun, Sister Simone Campbell, on Comedy Central's "Colbert Report" on Monday.

Such support has been “very affirming,” Mock told reporters after the meeting.

On June 1, LCWR's board rejected the Vatican criticism as  “unsubstantiated,” saying it led to “greater polarization” within the church. Similar pushback has been voiced by a group of Franciscan friars in the U.S., and the umbrella group representing men's religious orders, the Conference of Major Superiors of Men, offered the nuns their "prayerful support."