Singh also said India looked forward to welcoming Palestine as an "equal" member of the United Nations where the United States has threatened to veto any resolution seeking full United Nations membership for it.
Hours before Singh made the remarks on the Palestine issue in his address at the UN General Assembly, Foreign Secretary Ranjan Mathai said there is no change in India's "well-established" position on the Palestinian statehood, which it recognised way back in 1988.
"India is steadfast in its support for the Palestinian people's struggle for a sovereign, independent, viable and united state of Palestine with East Jerusalem as its capital, living within secure and recognizable borders side by side and at peace with Israel."
"We look forward to welcoming Palestine as an equal member of the United Nations," Singh said.
The Prime Minister also said the unresolved Palestinian question was a source of great instability and violence.
Mathai told reporters, "Our position on Palestine issue is well-established and well-known. As far back as 1988 we recognised Palestine state and there is no change in it." UN Secretary General Ban Ki-moon has forwarded the Palestinian application for recognition of a statehood to the President of the Security Council.
The US has vowed to veto the unilateral Palestinian bid at the Security Council, saying talks between Israel and the Palestinians are the only real path to peace and statehood.
For the Palestinians, full membership depends on nine approved votes in the 15-member Security Council as well as concurrence of the five permanent members. India is among the non-permanent members.
Palestinian Authority President Mahmoud Abbas met Ban just before he addressed the UNGA on Friday and submitted his application for Palestine to be admitted as a full member of the world body on the basis of June 4, 1967 borders with Jerusalem as its capital.