ANNAPOLIS, Md., June 19 — The presidents of dozens of liberal arts colleges have decided to stop participating in the annual college rankings by U.S. News and World Report.

The decision was announced Tuesday at the end of an annual meeting of the Annapolis Group, a loose association of liberal arts colleges. After two days of private meetings here, the organization released a statement that said a majority of the 80 presidents attending had “expressed their intent not to participate in the annual U.S. News survey.”

The commitment, which some college presidents said was made by a large majority of participants, represents the most significant challenge yet to the rankings, adding colleges like Barnard, Sarah Lawrence and Kenyon to a growing rebellion against the magazine, participants said.

U.S. News says it provides a valuable service to parents and students in its yearly evaluations, which are based on factors that include graduation and retention rates, assessments by competitors, selectivity and faculty resources. Critics say the ranking system lacks rigor and has had a harmful effect on educational priorities, encouraging colleges to do things like soliciting more applicants and then rejecting them, to move up the list.