He did not directly respond to a reporter's questions about the two situations at a news conference on Friday, saying only: "I want to know specifically more in cases like that and that is what we are looking factually into it today."
"Any time a group of people are identified and then excluded based on faith is a matter of concern to us and to the global religious freedom community," he said in general terms about Assam citizenship issue.
About 1.9 million people in Assam have not been included in the National Register of Citizens for the state that was published in August and they had 120 days to appeal their exclusion.
Many of them are said to be Muslims.
Hindus and other minorities like Christ, Sikhs and Buddhists who are not found to be citizens will be eligible for asylum in India.
The Pakistani journalist who asked the question said that Muslims were discriminated against.
About the general restrictions in Kashmir impacting people's ability to pray in mosques, Brownback said: "We believe that people should be allowed to freely practice their faith wherever they are and whoever they all are as long as they are peacefully practising their faith.
"That applies everywhere all the time and I will be raising these issues. Again, these are things that we will try to get all the factual setting and then try to raise them in constructive ways whenever we can and however we can."
(Arul Louis can be contacted at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )