"Talk now. You have to talk now and talk to stakeholders and talk to everyone," he told reporters here.
He said Pakistan had to be brought on board, too.
"Even if you are bitter with Pakistan, you have to talk to Pakistan. You have to bring them on board," he said.
The former chief minister, who won the recent bypoll to the Srinagar Lok Sabha constituency, said the government should not wait for a "conducive atmosphere" before starting the dialogue.
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India, he stressed, stood for the rights of the people. Denying those rights would create "further wounds and alienation" among the people of Kashmir.
"We are digging the grave of democracy if we do not talk," he warned, and called for "respecting" the Indian Constitution.
"Why do they not respect the Constitution that they swear by? You ban internet, you ban whatever you have...You are not going to win the war of hearts by banning these things."
Abdullah said that for two years, there was talk about a dialogue with all stakeholders, including the Hurriyat. Former chief minister Mufti Mohammad Sayeed had also said that talks would be held with Pakistan, he added.
"But nothing happened," he said. "It is wonderful that the Prime Minister and the Chief Minister have met, (but) they must have discussed more than what we know."
He referred to the CM's comment today that stone-pelters had to stop throwing stones for the talks to take place.
"Days before that, she said this gun culture must stop (and) then we will talk," he said. "These things are not going to end."
Asked if he endorsed stone-pelting, Abdullah replied that he supported the people as they were fighting for their rights which had been denied to them.
"What are they fighting for? They are not fighting for the Chief Minister's post, MP's post or MLA's post. They are fighting for the rights of the people," he said.
"They had a discussions in (former Prime Minister A B) Vajpayee's time, (former deputy prime minister L K) Advani's time, also met (the separatists) and certain recommendations were made. But nothing was done," he said.
The former Union Minister said the government had to be sincere in wishing for a dialogue. "Otherwise, if it is just to buy time, then it is going to be a failure. AFSPA will also be settled once you have peace."
"I feel sad, really sad that our children are going to suffer and they are not going to be able to get their education," he said. "Education is the basis of tomorrow."
Reiterating his call for Governor's Rule in the state, Abdullah said if the government had been able to "serve and deliver", he would not have made this demand.
He said his party would support any decision of the central or state government for the prosperity of Kashmir, but not side with them if the decision was going to be destructive.