Frank Gill, 64, New Zealand's ambassador to the United States, died of cancer today at a hospital in Auckland, N.Z.

Mr. Gill underwent surgery for bladder cancer in New Zealand in March 1980. After recovering he was named in August of that year to represent his country here.

He became ill again in Washington early this year and was admitted Feb. 16 to Georgetown University Hospital. After tests revealed cancer of the liver, he was flown home.

A third generation New Zealander, Thomas Francis Gill flew Hurricane fighter planes for Britain's Royal Air Force during the Battle of Britain in World War II. Later, he flew on night bombing raids for the RAF bomber command.

After the war he served in the Royal New Zealand Air Force, rising to the rank of air commodore.

From 1957 to 1959 he headed the New Zealand Joint Services Missions here. He retired in 1965 and was elected to parliament four years later. He served as minister of health and immigration and minister of defense before being named ambassador.

Mr. Gill held the Distinguished Service Order and was a Commander of the Order of the British Empire.

In addition to his wife, Barbara, survivors include three daughters, all of New Zealand.