ALBANY -- Stepping up previous warnings, leaders of the State Senate and Assembly called for a two-year delay Tuesday in using Common Core test results to make evaluations about teachers, principals and students.

The leaders also called for delaying the sharing of student information with a private "cloud-based" data firm until privacy and security concerns were "fully satisfied."

The announcement by Assembly Speaker Sheldon Silver (D-Manhattan) and Senate co-leaders Dean Skelos (R-Rockville Centre) and Jeff Klein (D-Bronx) effectively tells the state Board of Regents, which sets education policy in New York, to slow down implementation of the new Common Core academic standards or the legislature will.

Their specific demand for a two-year delay -- "at minimum" -- intensified previous calls from legislators to simply delay implementation.

"I think we have their attention," Silver said, referring to the Regents. He said legislators are "telling them: Now's the time" to act.

"If the Board of Regents doesn't deal with it appropriately, then the legislature will have to," Skelos said in a separate interview.

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Gov. Andrew M. Cuomo has called the Common Core implementation "flawed" and appointed a panel to review the rollout. Cuomo spokeswoman Melissa DeRosa said, in response to legislators, "It would be premature to consider any moratorium before the panel is allowed to do its work."

The Regents have said before that they intend to address the issue in February. Regents Chancellor Meryl Tisch and Education Commissioner John B. King Jr. reiterated that plan in a response to Silver, Skelos and Klein, saying next week they will consider "a series of possible options that reflect the input the board has received from legislators and the public to make thoughtful adjustments to Common Core implementation."

Any moratorium would also impact the state's new teacher-evaluation law, which is tied to the new Common Core assessments in statute, an Education Department official said.

Perhaps coincidentally Tuesday, legislators began interviewing applicants for four spots on the Board of Regents. Silver didn't say whether incumbent Regents should be reappointed but added "how they respond" to the Common Core issue "will be significant to their re-election."

The Regents are elected by the legislature. Because of the "one person, one vote" process used for Regents, Silver's Democratic-dominated Assembly effectively controls the selections. This year, two at-large seats are up for election, as well as Albany- and Staten Island-based seats.

Legislators also criticized a state plan to turn over records of 2.3 million New York students to inBloom Inc., an Atlanta-based nonprofit that maintains a computerized "cloud"-based database.