The Arizona Republican recalled the general, who died Friday at age 102, in an article published Sunday in The Wall Street Journal.
McCain said he met the general twice, once briefly in 1967 while being held as a prisoner of war and again in the 1990s, after McCain had been elected to the U.S. Senate.
While Giap had a reputation during the war as a "ruthless fighter with a fierce temper," during their second meeting McCain said, "both of us clasped each other's shoulders as if we were reunited comrades rather than former enemies."
McCain said he assumed Giap, who was by then retired from the Ministry of National Defense, would want to talk about the war years. Giap, however, dismissed such a conversation, saying, "That is all in the past now. You and I should discuss a future where our countries are not enemies but friends."
Giap's victories, the senator wrote, were achieved by "a patient strategy" that involved "an unwavering resolve to suffer immense casualties and the near total destruction of their country to defeat any adversary."
That strategy succeeded, McCain said.
"The U.S. never lost a battle against North Vietnam, but it lost the war," McCain said. "Countries, not just their armies, win wars. Giap understood that. We didn't."
"Americans tired of the dying and the killing before the Vietnamese did. It's hard to defend the morality of the strategy. But you can't deny its success," McCain said.
Notable deaths of 2014 [PHOTOS]