John Allen Chau had hoped to convert members of the Sentinelese people when he illegally travelled to North Sentinel Island - a remote Bay of Bengal island under the jurisdiction of India.
Samuel Brownback was quoted by the Indo Asian News Service as saying: "The US government has not asked or pursued any sort of sanctions that the Indian government would take against the tribal people in this case.
"It's a tragic situation and a tragic case of what's happened, but that's not something that's been asked."
The 26-year-old from Alabama had studied at Oral Roberts University - a Christian institution in Oklahoma. He was also involved with the global mission society All Nations.
In a letter to his parents prior to his death, Chau said: "You guys might think I'm crazy in all this, but I think it's worth it to declare Jesus to these people.
"Please do not be angry at them or at God if I get killed. Rather, please live your lives in obedience to whatever He has called you to and I'll see you again when you pass through the veil."
Attempting to recover John Allen Chau's body from the #Sentinelese carries terrible risks for everyone involved, and shouldn't be attempted. @Survival Director @StephenCorrySvl's statement here: https://t.co/smyQiBgOia
— Survival International (@Survival) November 26, 2018
Earlier this week, Premier reported how Mr Chau's father blamed "extreme Christianity" for pushing his son to a "not unexpected end".
The international organisation Survival is among those who warns of the dangers - which include the threat of disease - of interaction with remote tribes.
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