Three respected Catholic publications are reporting that Cardinal Bernard F. Law, the controversial former Boston archbishop, played a key role in the Vatican’s decision to tighten its grip on the largest association of Catholic nuns in the United States.

The Vatican announced its initiative on April 18, naming three American prelates to ensure that US nuns conform to Church doctrine, which has grown more conservative under Pope John Paul II and his successor, Pope Benedict XVI.

Earlier this week, a columnist for The Tablet, a British Catholic weekly, reported that the Vatican’s initiative was sparked by Archbishop William E. Lori, who was recently named to lead the Archdiocese of Baltimore, who “formally petitioned’’ the Congregation for the Doctrine of the Faith to investigate the nuns.

The Tablet also reported that Law was “the person in Rome most forcefully supporting Bishop Lori’s proposal.’’

But Lori denied the first of those assertions in a statement issued to the Globe yesterday through the United States Conference of Catholic Bishops.

“Bishop Lori did not petition the CDF to conduct the current doctrinal assessment of the [Leadership Conference of Women Religious], nor would it have been appropriate for him to do so,’’ the statement said.

The statement did not address any role that Law might have played in the move to rein in the Leadership Conference, which represents 57,000 nuns, or 80 percent of those in the United States.

Sandro Magister, writing in an Italian publication, and John Allen of the National Catholic Reporter also reported that Lori and Law used their influence to help initiate the Vatican’s actions against the nuns, although those reports were less specific about their actions.

And the US Conference of Catholic Bishops appeared to at least partially confirm those reports in a second statement to the Globe.