Hardline Hurriyat leader Syed Ali Shah Geelani trashed the Centre's eight-point formula to bring peace to Kashmir, saying the package was "a mere eyewash".
The Geelani faction has issued a new protest calendar from September 27 to October 6.
"This is not a positive approach to solve the Kashmir issue. They have not addressed our basic demand of accepting Kashmir as (disputed territory). What they have announced is far less than what we had demanded," Geelani said.
However, Chief Minister Omar Abdullah welcomed it as a "good first step".
"The most important point is engaging interlocutors. This brings the political focus back on Kashmir; so far the focus has been economic," he told HT.
Abdullah was also happy that the Centre had thought of reducing its security presence.
The chief minister said the police had been instructed to review all the cases against stone throwers. "We held a meeting today (Saturday) about schools resuming classes from Monday," Abdullah said.
The Mirwaiz wing of the Hurriyat Conference said the organisation had been stressing "the implementation of certain measures for improving the ground situation and creating an atmosphere free of intimidation and coercion … A serious and sincere effort needs to be made". But the Mirwaiz wing spokesman said the package would be discussed at a meeting.
Some among separatists, who were vocal about human rights violation during the meeting with 39 parliamentarians, chose not to react. "We will call a meeting of our working committee and executive council before taking a position," said JKLF chairman Yasin Malik.
The main opposition People's Democratic Party gave a guarded reaction.
"It is a good beginning, and can help in reviving the peace process ... But a serious follow-up (is needed)," said party spokesman Nayeem Akhtar.