Australian Ambassador F. Rawdon Dalrymple warned last night that U.S. failure to urge France to stop nuclear testing in the South Pacific will erode American influence in the region and threaten the already troubled Australia-New Zealand-United States alliance (ANZUS).

"If you want the South Pacific to become an area where the Soviet Union, Cuba and others of that stripe can find fertile ground for anti-United States, anti-West propaganda, and in which they can develop activities directly prejudicial to our interest, then continue with a policy of indifference to what the French are doing there," Dalrymple said in a speech to the Asia Society here.

The speech, which apparently echoed the views of Prime Minister Robert Hawkes' government, followed France's admission that its agents were responsible for sinking an antinuclear protest ship in New Zealand waters last July.

The widening scandal over destruction of the Greenpeace ship Rainbow Warrior has underscored the strong sentiment spreading through the South Pacific, from Australia and New Zealand to the tiny islands of Micronesia, for an end to all nuclear activities there.

The United States is embroiled in a dispute over New Zealand's determination to bar nuclear-armed or nuclear-powered ships from its ports that has halted military cooperation between the two countries and paralyzed ANZUS as an effective strategic alliance.

Dalrymple's speech was a reminder that Hawke, whom Washington regards as a faithful and reliable ally, might find it increasingly difficult to fend off pressures from antinuclear elements in his Australian Labor Party if the United States is seen as indifferent to regional opinion.

The Reagan administration, whose practice has been to condemn terrorist acts quickly and unequivocally, has been silent in the wake of France's admissions. State Department spokesman Peter Martinez yesterday answered a succession of questions about U.S. views on the Rainbow Warrior incident by repeatedly saying, "No comment."

Dalrymple, while not mentioning the incident, said bluntly that the United States is seen throughout the South Pacific as siding with France for fear of angering an important European ally.

"Continued French use of Mururoa Atoll [a French possession] for nuclear testing is absolutely certain to prejudice the South Pacific people against the West, against the United States and Australian interests in a way that will quite possibly prove very costly," the ambassador said.