Jammu and Kashmir Chief Minister Mufti Mohammed Sayeed and the All Party Hurriyat Conference on Tuesday welcomed Pakistan President Pervez Musharraf's proposal for ceasefire along the LoC and Kashmir.
India, however, on Tuesday evening rejected Musharraf's proposal.
The Hurriyat also said militants will have to be taken into confidence for durable peace, which can lead to a sustained dialogue process on the Kashmir issue.
The outfit's chairman Maulana Mohammad Abbas Ansari said there should be sincerity on both sides while initiating a dialogue process to resolve the Kashmir issue in which the militant leadership should also be involved.
Ansari said people on either side of the Line of Control in Jammu and Kashmir should be allowed to meet which would go a long way in building a conducive atmosphere for talks and for them to succeed.
Asked if Hurriyat would be able to convince the militant leadership to hold their guns while talks were in progress, Ansari said Hizbul Mujahideen chief Syed Salahuddin has also called for a ceasefire, but with certain conditions.
"Mujhe aam khanay se garaz hai, paed ginnay sey nahin (I want to eat mangoes, why should I count the trees). If anyone can pursue the Kashmir cause and put an end to the bloodshed, we will support him," he said.
Sayeed welcomed the ceasefire proposal stating it could help bring down the number of casualties in cross-border firing round the year.
"This is an important step as there were a number of casualties, including civilians every year in cross border firing along the LOC," he said.