Afghan forces, beset by record casualties, desertions and "ghost soldiers" who do not exist on the pay rolls, have been struggling to rein in the Taliban since US-led NATO troops ended their combat mission in December 2014.
Thousands of extra coalition troops were needed to break the war out of a stalemate, Nicholson, the top US commander in Afghanistan, told the US Congress on Thursday, in what could be President Donald Trump's first major test of military strategy.
"The war in Afghanistan is a war against terrorism and we want this war to reach a successful end. In that regard we think this is a positive step."
There are currently more than 13,000 NATO troops -- including 8,400 US forces -- deployed to Afghanistan for training and counter-terrorism purposes, down from a peak of about 140,000 in 2011.
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Trump would seek the advice of Defense Secretary James Mattis before deciding on Nicholson's request for reinforcements, White House press secretary Sean Spicer told reporters.
The White House said the pair spoke again on Thursday to "discuss opportunities to strengthen the bilateral relationship in areas such as security, counterterrorism cooperation".
The debate over troop numbers underscores concerns over the worsening security situation in Afghanistan, with insurgents threatening several provincial capitals amid anxiety that Pakistan, Russia and Iran were actively propping up the militants.
Aside from additional troops, a holistic review of the US war strategy in Afghanistan, including sustained pressure on Pakistan to end insurgent sanctuaries on its soil, is vital, local observers say.