According to al-Furat news website, the political office of the NWT said in a statement that the movement itself was among the groups seeking the premiership of Zurfi but objects to the way he was named as prime minister-designate.
It said that in the selection process, the views of many major political groups were unheeded.
The statement went on to say that the NWT underlines the need for bringing different views closer together in order for the country to get out of the current political crisis.
Iraq’s President Barham Salih on Tuesday designated Zurfi as prime minister tasked with forming a government within 30 days.
Some political groups had earlier voiced opposition to such a move.
Zurfi is a former official of the US-run authorities that took over Iraq after the 2003 US invasion that deposed Saddam Hussein.
He is head of the Nasr parliamentary grouping of former prime minister Haider al-Abadi.