"Any kind of solution... must be acceptable to all regions of J&K and to all sections of J&K people, and it should have complete endorsement of public opinion as is expressed in Parliament of India and only then can we carry things forward," he told reporters in Jammu before leaving for Delhi along with another interlocutor, Radha Kumar.
The interlocutors stressed that they had made a "modest" beginning to a "long and arduous" journey.
"We are at the beginning of a journey which is going to be long and arduous one and we are prepared for it," Padgaonkar said.
In reply to a question on the interlocutors' proposed meeting with Bharatiya Janata Party leader L K Advani in New Delhi, he said there were a lot of people whom they could not meet because they were away for elections.
"We will go and brief the government and opposition parties. We are also seeking an appointment with the (members of) the all party delegation to give them impressions about what we heard and what we learned in Srinagar and Jammu," he said.
The BJP has been critical of Padgaonkar's comments that Pakistan has to be involved while finding a permanent solution to the Kashmir issue.
"This is only the first visit to try and learn complexities in the J&K situation and we will share our impressions with them," Padgaonkar said. "We will also seek their insights about how to proceed."
"This not an event but a process and the process is going to take a long time to fructify," Padgaonkar said.
On the proposed talks with Advani, he said he cannot discuss the details as these are briefings and exchange of ideas.
"Our determination is to go and tell political leaders back in Delhi of what we have gathered," he said. "So it is completely premature to formulate opinions as we are in the process of understanding and listening people which is our mandate."
In response to a query whether they had visited Kot Bhalwal jail in Jammu to meet separatist leaders Shabir Shah and Abdul Qayoom, Padgaonkar said, "That is not correct but we went to the jail to get details of detenues who have been there for militancy related reasons and to find from the jail as to where their cases stood."
He said the jail superintendent provided them with comprehensive details about these aspects.
Padgaonkar emphasised that the three-member panel of interlocutors will not meet anyone "unless they invite us".
"We have said time and again that anyone who wishes to speak to us, we will be happy to speak to them," he said, "If they chose not to speak to us, I am sure they have constraints or compulsions".
Replying to a question on her suggestion to amend the Constitution, Kumar denied that she had said so. "It was fabricated."
"What I did say is that Indian Constitution is a very beautiful one and I am very found of it and it has demonstrated flexibility time and again," she said.
Kumar said, "If there is some agreement by all parties on some new solution, I am sure the Indian Parliament would be happy to consider it."
"You know the history of our Constitution which took five years of debate all over the country and if you read those constitutional debates I can tell you as an Indian you will be so proud."
Emphasising that their task was to start the dialogue process, Kumar said, "We believe that we have made a modest beginning to that end and nothing can deflect us from that purpose."
On aazadi, she said, "It is a very very flexible and nuanced term which has many meanings for different people. One of our tasks will, no doubt, be to explore these nuances in the coming months."
Replying to a question on whether any roadmap has been prepared, Kumar said, "People came to us with ideas and we suggested that the next time these could be discussed in greater detail."
"The task of preparation of the roadmap has been entrusted to us," she said.
Kumar also said that it was a short but rich trip for them as they met a large number of people in Jammu. "Our focus was on migrants and their aspirations. We also met some political parties and linguistic and religious groups."
"Next time we want to spend 4-5 days in Jammu and also go to different districts in Jammu division," she said.