The Biden Administration has engaged with the Indian government on a number of occasions urging them to cooperate with Canada in its investigations into the death of a Khalistani separatist, a US State Department official has said.

Bilateral ties between India and Canada came under severe strain following Canadian Prime Minister Justin Trudeau's allegations of "potential" involvement of Indian agents in the killing of Hardeep Singh Nijjar in British Columbia in June.

India has rejected the allegations as "absurd" and "motivated" and expelled a senior Canadian diplomat in a tit-for-tat move to Ottawa's expulsion of an Indian official over the case.

The issue of the killing of Nijjar in Canada was raised by Secretary of State Antony Blinken during his meeting with External Affairs Minister S Jaishankar here last week.

"As he made clear then, I'll reiterate now, we remain in close coordination with our Canadian colleagues on this question," State Department spokesperson Mathew Miller told reporters on Monday at his daily news conference in response to a question raised by a Pakistani journalist.

"We have engaged with the Indian government on a number of occasions to urge them to cooperate with Canada's investigation. The secretary had an opportunity to do that in his meeting with the foreign minister on Friday," he said.

When asked if India has agreed to cooperate with Canada, Miller said this is for New Delhi to respond to.

"I will let the Indian government speak for themselves and I will speak for the United States government, and we urge that cooperation," he said.

Jaishankar told journalists here last week that the governments of India and Canada will have to talk to each other and see how they resolve their differences over the issue and underlined that the larger issue of "permissiveness" must be flagged and addressed.

"The issue is as follows, which is that the Canadians have made some allegations. We have pointed out to them that this is not the government of India's policy, but if they are prepared to share with us specifics and anything relevant, we are also open to looking at it. So in that sense, that's where the matter stands," Jaishankar said.