Abbas's statements came in a joint press conference he held with India's Prime Minister Narendra Modi, who was on his first ever visit to Palestine.
Abbas said "we count on India's role, as a world power with significant weight and status to contribute to achieving just and aspired peace in our region, due to its impact on world security and stability."
Abbas stressed that Palestinians have "never rejected negotiations any day; we were and still are ready for it, and believe that forming a multilateral mechanism of several states is the best approach to overlook those negotiations."
Modi said he is "proud to be renewing friendship and support to Palestine" and that his country "holds on to the nobility of the Palestinian people's interests" and hoped for establishing the independent Palestinian state by peaceful means.
He highlighted that the support for the Palestinian cause has been a steady point in India's foreign policy.
The two countries signed four agreements worth 41 million US dollars in various sectors, including education, health, media and women economic empowerment.
Abbas gave Modi the highest medal of the state of Palestine as a sign of valuing friendship with India.
Prior to this visit, Modi said that he has "de-hyphenated" relations with Palestine and Israel, establishing "mutually independent and exclusive relations with both partners."
India's relationship with Israel has seen a significant development in the past few years, crowned with a recent multi-million dollars deal with Israel in military and hi-tech sectors.
Modi made his first ever visit to Israel in July last year, and Israeli Prime Minister paid back the visit last month.
India was one of the 120 UN member states that voted in favor of Palestine in the UN General Assembly resolution calling on the US to retract its recognition of Jerusalem as Israel's capital last December.