The insurgents were responding to a statement Wednesday by senior Russian diplomat Zamir Kabulov, who said his country was exchanging information with the Taliban about the group.
Kabulov, who is a Kremlin special representative in Afghanistan, said Moscow had a shared interest with the Taliban in counteracting the spread of the Islamic State group -- also known as Daesh.
We "do not see a need for receiving aid from anyone concerning so-called Daesh and neither have we contacted nor talked with anyone about this issue," the Taliban said in an English-language statement on their website.
Although there are signs that the popularity of IS is growing in Afghanistan, including a radio station that broadcasts Islamic State propaganda every morning, the Taliban remain a far more potent force.
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The Taliban in their statement played down reports of an IS presence.
"Some people in Afghanistan are wrongfully taking advantage of the name Daesh while national and international intelligence are also supporting them with the aim of prolonging the occupation," they said.