"For now I can tell you there was nothing new in his speech and it was very unclear," Zabiullah Mujahid, a spokesman for the Taliban in Afghanistan, told AFP.
He added that the militants were preparing a formal statement which would be released later.
Trump backtracked from his promise to rapidly end America's longest war in his first formal address to the nation as commander-in-chief late Monday, though he did not offer specifics.
A senior Taliban commander told AFP that Trump was just perpetuating the "arrogant behaviour" of previous presidents such as George Bush.
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"He is just wasting American soldiers. We know how to defend our country. It will not change anything.
"For generations we have fought this war, we are not scared, we are fresh and we will continue this war until our last breath," he told AFP by telephone from an undisclosed location.
He added that the statement proved the current Afghan government "is a US puppet".
The rocket landed in a field in the city's diplomatic quarter, with no casualties reported.
While Trump refused to offer detailed troop numbers, senior White House officials said he had already authorised his defence secretary to deploy up to 3,900 more troops to Afghanistan.
He also lambasted ally Pakistan for offering safe haven to "agents of chaos."
A commander from the Taliban-allied Haqqani network, long believed to have links to Pakistan's shadowy military establishment, told AFP that Trump "has proved it's a Crusade".
Prior to Trump's announcement the Taliban had written an open letter warning him not to send more troops and calling for the complete withdrawal of foreign forces from Afghanistan.