Abbas met Minister of State for External Affairs Shashi Tharoor Friday - a day after he had a dinner meeting with Prime Minister Manmohan Singh shorty after his arrival in New Delhi.
Tharoor reassured the visiting Palestinian leader of New Delhi's support for peace and development in the Middle East.
"We would like to see Palestine and Israel living side by side behind secure borders in prosperity and peace. Where we can be helpful is certainly something we continue discussing with our friends," Tharoor told reporters after the meeting.
"(I had an) excellent meeting with President Abbas and (Foreign Minister Riyad al) Maliki of Palestine," Tharoor later wrote on micro-blogging site Twitter.
Tharoor said he had a "thorough discussion" on the political situation and peace process in the Middle East. He also assured Abbas and Maliki of "Indian help for Palestine".
Abbas arrived in New Delhi Thursday on a two-day unannounced visit to India. His visit comes in the wake of a controversy after a leading Israeli television channel broadcast a tape showing Abbas' aide allegedly trying to receive sexual favours from a Palestinian woman.
Abbas Thursday night met Manmohan Singh who announced $10 million as budget support to the Palestinian National Authority and reassured Abbas of India's support for economic and social development.
Manmohan Singh in his meeting with Abbas reiterated "India's commitment to the Palestinian cause in line with United Nations Security Council calling for a sovereign, independent, viable and united state of Palestine", a ministry of external affairs spokesperson said.
Manmohan Singh hosted dinner for Abbas and his delegation. The two leaders held discussions on the fresh efforts at initiating a peace process in the volatile Middle East region.
"They also discussed the Russian proposal for a meeting of the European Union, Russia, the United Nations and the US (the Quartet working for peace in the Middle East)," the official said.
The visit of the Palestinian president comes about a fortnight ahead of Manmohan Singh's visit to Saudi Arabia.
India has been supporting a peaceful resolution of the Middle East conflict. In 1974 it recognised the Palestine Liberation Organisation as the sole representative of the Palestinian people. India in 1988 became the first non-Arab country to recognise the state of Palestine.
About the visit, Malki said: "The idea is really to brief the (Indian) leadership about the political situation and also to listen from them their advice."
"Of course we are focused on our bilateral relations. Our bilateral relations are excellent
but still, you know, we are keen to even deepen further such relations, and we have discussed many potential areas of cooperation in the future," he added.
The visiting leaders left for Islamabad in the evening on their way back to home.
