Hurriyat leaders Syed Ali Geelani and Mir Waiz Umar Farooq said that the prime minister had raised his voice for political rights of the Kashmiris.
They added that Nawaz Sharif has proven that he was a well-wisher of the Kashmiris.
Calling for an independent investigation into Kashmir was a sensible way of taking things forward, they said.
They added that the speech in the UN reflected sentiments of Kashmiris.
Prime Minister Nawaz Sharif on Wednesday addressed the UN General Assembly where he highlighted the Kashmir issue.
He demanded an independent inquiry into the extrajudicial killings in Kashmir and an end to the curfew.
Nawaz Sharif said that over a hundred Kashmiris have been killed, hundreds, including children and infants, blinded by shotgun pellets and over six thousand unarmed civilians injured over the past two months.
The premier demanded a UN fact-finding mission to Kashmir to take stock of extra-judicial killings. He also called for a UN-backed plebiscite and demilitarisation of Jammu and Kashmir.
Prime Minister Nawaz Sharif met the United Nations (UN) Secretary General Ban Ki-moon and handed him dossiers containing evidences of brutalities in Indian-occupied Kashmir (IoK) by occupying Indian forces.