"State Department, on behalf of US Govt, expressed condolences and assured they are working with all agencies concerned to ensure speedy justice," the Indian Embassy in the US said in a series of tweets.
Patel, 43, the owner of a convenience store in Lancaster County, South Carolina, was found dead of gunshot wounds in the front yard of his home on Thursday.
Rai, 39-year-old Sikh, has been shot outside his home by a partially-masked gunman who shouted "go back to your own country", in a suspected hate crime.
Mr Sarna also "underlined" the need to prevent such incidents and protect the Indian community.
In the case of Patel, the County Sheriff had pointed out that this may not be a hate crime. "We will remain in touch with them," an Indian Embassy source said.
There have been a slew of bias-related incidents in the US, raising concerns over the safety of the members of the Indian-American community.
Last month, 32-year-old Indian engineer Srinivas Kuchibhotla was killed when 51-year-old US Navy veteran Adam Purinton opened fire at him and his friend Alok Madasani, yelling "get out of my country".