Prime Minister Malcolm Fraser says he has resolved not to let President Reagan have his way on everything when the two conservatives meet for the first time at the White House Tuesday.

In an interview before he left here for Washington, Fraser said he plans to take strong positions in his talks with the Reagan administration, breaking with what is seen here as a tradition of Australian leaders mumbling thanks to American presidents.

"Where the United States is right, we'll support her and support the U.S. president strongly," he said. "But that does not mean to say that we'll support the U.S. in all things. Quite patently, we won't."

Fraser said he will withhold commitment that Washington has sought on an Australian contribution to the peacekeeping force being put together under U.S. auspices to patrol the Sinai Peninsula after final Israeli withdrawal scheduled next April.

The opposition Labor Party opposes any Sinai force not run by the United Nations. Within Fraser's government -- a coalition of his urban-based Liberal Party and the rural-based Country Party -- the Country Party bitterly opposes any Australian initiative in the Middle East.

Rural Australians export lamb, grain and wool to Arab countries. They fear some Arab nations would move against Australian trade if Australian troops were used to police a treaty most Arab governments oppose.