Most Americans think that President Reagan is in good health and will be fully able to carry out the responsibilities of his office for the rest of his term despite his operation for cancer of the colon less than three weeks ago, according to a new nationwide Washington Post-ABC News Poll.

Twenty-one percent of those surveyed said they think that Reagan will not be able to complete his term for one reason or another. Seventy-five percent said the president would finish his term, and 4 percent offered no opinion.

Those figures show virtually no change since January, before the president's second inauguration and long before it became known that he had cancer. At that time, 20 percent in a Post-ABC News poll said they did not expect Reagan to complete his second term.

Reagan's return to the White House seven days after his operation and his confident demeanor appear to have convinced the great majority that he is in extraordinarily good shape. The public appears to be taking Reagan at his word when he says, as he did several days ago, "I had cancer." Sixty-two percent in the survey see the president as being in above-average health for a person his age, which is 74; 32 percent say he is in average health. Only 5 percent consider his health to be below average.

On the question of whether Reagan will be cancer-free for the remainder of his term, 54 percent expect no recurrence of the disease while he is still in office; 33 percent think that there will be one, and 12 percent have no opinion.

At the same time, seven of every 10 people interviewed believe that Reagan will be healthy enough to carry on his duties to the fullest through 1988. Nine percent in the survey say Reagan should resign and let Vice President Bush take over; 88 percent reject that idea, and 3 percent offer no opinion on it.

The survey was conducted Thursday through Monday, with a random sample of 1,506 adults interviewed by telephone in the continental United States. About one-third said someone in their immediate family has had cancer, and in a majority of cases that cancer victim has died.

There are virtually no differences in views about Reagan's health among those whose families have been touched by the disease and the rest of the population. To the same extent, both groups expect him to serve out his term and do not consider him too old to be president.

Four percent of those surveyed said they have had a checkup for cancer, or scheduled one, since Reagan's operation. But only 9 people in the survey -- six-tenths of 1 percent, about 1 million people nationwide -- said they were influenced to do so by the president's operation.