Moderate Kashmiri separatists have welcomed an offer of talks by the Indian Government but say they will try to build a consensus before entering a dialogue with Delhi.
They will consult separatist groups and the public before meeting Deputy Prime Minister LK Advani, a spokesman said.
Separatist leader Moulvi Abbas Ansari has already welcomed Delhi's initiative
The offer from Delhi has been rejected by hardliners in the divided separatist movement, as well as by militant groups fighting Indian rule in Kashmir.
India's surprise announcement on Wednesday was followed by another one unveiling a series of steps to improve ties with long-time rival, Pakistan.
The moderate faction of the All Party Hurriyat Conference - the main separatist alliance in Indian-administered Kashmir - held a meeting of its executive committee in the state's summer capital, Srinagar, on Thursday.
A spokesman, Abdul Gani Bhat, said after the meeting that "talking is better than acrimony" and would help find a solution to the long-running dispute.
"As for the offer of talks the [Hurriyat] has decided to procure a broader consensus.
"We will be therefore talking to groups inside... and outside Hurriyat," he said.
But a hardline breakaway separatist group of the Hurriyat led by Syed Ali Shah Geelani described Delhi's move as futile.
Mr Geelani, who favours closer ties with Pakistan, says talks without the inclusion of Islamabad would have little meaning.
Armed militants fighting Indian forces in Kashmir dismissed the Indian Government's offer, saying it was a ploy.
Sayed Salahuddin, the head of the Hizbul Mujahideen, one of the leading militant groups in the state, said talks without including Pakistan was a "delaying tactic" rather than an effort to find a solution.
Mr Salahuddin, who is based in Pakistan-administered Kashmir, said Delhi was trying to sign an accord with the moderate wing of the Hurriyat to create hurdles for the armed struggle.
Two other groups, Al Nasirin and Farzandan-e-Milat, warned the Hurriyat against "walking into the trap laid by the Indian Government".
Al Nasirin asked the Hurriyat leaders to consult the militant commanders before arriving at a decision.
Peace with Pakistan
On Wednesday India proposed resuming cricket ties and boosting transport links with Pakistan.
Islamabad said it would respond positively but expressed disappointment that the proposals did not include a direct dialogue on Kashmir.
The United States and Britain have both welcomed India's proposals to build links with Pakistan.
"Such steps will help to build greater confidence and trust between India and Pakistan," British Foreign Secretary Jack Straw said.
The US said it was a major step towards "normalising relations".
Mr Sinha's offer to encourage what he called people-to-people contact comes amid mounting violence in Kashmir and follows several months of hostile rhetoric from leaders in both India and Pakistan.
Among the most dramatic of the 12 measures India suggested on Wednesday was the opening of the main highway linking Indian and Pakistani-administered Kashmir.
- Two new bus links, including one linking the divided Kashmir
- A ferry service between Bombay (Mumbai) and Karachi
- The resumption of full sporting ties, including cricket
- Free medical treatment for 20 Pakistani children in India
- And more talks on restoring air and rail links
However, Mr Sinha ruled out direct talks with Pakistan until Islamabad had ended "cross-border terrorism" in Kashmir.
Islamabad denies backing Kashmiri militants, saying it offers them only diplomatic and moral support.
India and Pakistan have fought two of their three wars since independence over Kashmir.