Swaraj, who is on her first visit to West Asia as the External Affairs Minister, reaffirmed India's consistent support for the Palestinian cause, emphasising that there has been "absolutely no change in its policy in this regard".
Swaraj was welcomed by Palestine's Assistant Minister of Foreign Affairs for Asia Ambassador Mazen Shamiyeh at the Bituniya Checkpoint as she crossed over from Israel to the Palestinian territory after arriving in Tel Aviv last evening.
"India's wisdom and political insight can be very useful in defusing tensions in the region," al-Maliki told Swaraj during their meeting here.
The Palestinian Foreign Minister also called India a "good friend on whom the Palestinians can rely for support in many areas".
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Describing India as "not just a friend but a brother", Abbas applauded New Delhi's consistent support for the Palestinian cause.
The two sides held substantive discussions on bilateral and regional issues with the Palestinian side briefing Swaraj on the developments in the peace process.
Swaraj and al-Maliki discussed initiating a joint commission at the ministerial level to take forward bilateral cooperation. Al-Maliki also briefed Swaraj on the situation in Syria, Yemen and Iraq, officials said.
Palestinians have expressed surprise at India's vote at a UN forum last year but said that they "understood" India's "principled position".
India, for the first time, last year abstained from voting on a resolution on Palestine adopted at the UN rights body that calls for accountability by parties involved in 2014's conflict in Gaza.
"No such issue was however raised in the meeting of the foreign ministers," Dr Wael al-Battrekhi, Palestinian foreign ministry's head of media department, told PTI.
"Happy to note Al Quds University will soon host an Indian Studies Chair and have linkages with Jamia Millia Islamia in India," Swaraj said.
Speaking at ceremony, she said India's strengths in IT services could benefit Palestinian economy and society. "We are ready to assist Palestine in IT and other sectors."
"We will build another Center for Excellence in ICT and Innovation in Gaza City and a Techno Park in Ramallah," she said.
"This is my first visit abroad in 2016 and Palestine is my first destination. India's solidarity with Palestinians and principled support to the Palestinian cause is rooted in our own freedom struggle," Swaraj asserted.
"The entire Indian political leadership remains steadfastly committed to these policies. We are working for closer political interaction and deeper economic and academic engagement with Palestine," she said.
"We must harness the experience of Palestinian students in India to further our friendship. India's empathy with the Palestinian cause and friendship with its people is undiluted and an integral part of our foreign policy," she added.
The President of Al Quds University Imad Abu-Kishk, applauding India's help and support, said India "is a true friend" of Palestinians right from the beginning "when it became the first non-Arab country to extend recognition to us".
President Abbas also hosted a lunch for Swaraj.
Swaraj's visit comes three months after President Pranab Mukherjee's historic trip to the region, the first by an Indian Head of State to the region.
During his talks with Swaraj, Al-Maliki also expressed gratitude for India's consistent efforts to boost capacity building process in Palestine.
India has been offering several scholarships every year to Palestinian youngsters, started a girls secondary school in the West Bank and the India-Palestine Digital Learning and Innovation Centre to equip the youth here with technical knowhow was inaugurated today.
India would also be building the Palestinian Institute of Diplomacy in Ramallah from a promised aid package of USD 17.89 million.
Earlier, Swaraj was given a red carpet welcome on her arrival in Tel Aviv yesterday by Israeli officials.