Albert Shanker, president of the 600,000-member American Federation of Teachers (AFT), yesterday issued his most scathing criticism to date of Education Secretary William J. Bennett, accusing Bennett of pushing the agenda of the New Right and saying the secretary is "not interested in secondary and elementary schools at all."

In an interview with United Press International, Shanker said he had high hopes for Bennett when he took office in January. But now, Shanker said, "I'm very disappointed. I think he's made a lot of blunders."

"I think what Bennett is doing is horrible and he ought to see it," Shanker said. "He has made a lot of headlines and almost all of the headlines have been blunders."

The criticism from Shanker is particularly damaging because the union leader had been considered generally supportive of Bennett, although the two differed on specific issues.

Bennett's chief of staff, Wendell Willkie II, said last night that Bennett and Shanker "have important areas of agreement as well as disagreement" and that Shanker's "harsh and intemperate" remarks "certainly do not contribute to a healthy national conversation on this vitally important subject."

When Bennett was first tapped to become education secretary, one of his first congratulatory phone calls was from Shanker. Since then, in what some union rivals have viewed as a drift to the right, Shanker has won praise from Bennett by advocating a national examination for new teachers, and by proposing that students be given some choice of attending public schools outside of their districts.

In his interview, Shanker specifically criticized Bennett for supporting merit pay for teachers, for advocating college student aid cuts, and as using his office as a bully pulpit to promote tuition tax credits and vouchers. An AFT official said Shanker sees his own "choice" proposal -- limited to public schools -- as an alternative to the Reagan tuition tax credit and voucher plans.