According to US intelligence officials, information that Russia offered bounties to Taliban militants for killing American troops was included in an intelligence brief for US President Donald Trump in late February.
The White House, however, has denied that Trump was briefed at that time, arguing that the intelligence was not credible enough to bring to his attention.
McKenzie said that while he could draw no direct link between any potential payments and US casualties, it's common that intelligence is not definitive.
"We should always remember, the Russians are not our friends," said McKenzie, who is travelling in the Middle East. "They are not our friends in Afghanistan. And they do not wish us well, and we just need to remember that at all times when we evaluate that intelligence."
He said there was no need to beef up security for troops there because the US already takes "extreme force protections measures" in Afghanistan.
"Whether the Russians are paying the Taliban or not, over the past several years, the Taliban have done their level best to carry out operations against us."
Just days after the February intelligence briefing, the US signed an agreement with the Taliban, mapping out the withdrawal of American forces from Afghanistan by May 2021.
The US pulled several thousand troops out this year, and now has about 8600 there.
- AP