Jaishankar, who arrived here on Sunday on a two-day visit, held a brief tete-a-tete, followed by delegation-level talks where bilateral and multilateral issues were discussed with Szijjarto.
"The visit is a major boost to India-Hungary bilateral relations with a packed Monday full of series of talks, agreements, meetings, press conference," the Indian embassy in Hungary tweeted.
"Happy to be back in Budapest. Good memories, great future. Thank FM Peter SzijjAirtA for a very positive and productive meeting. Look forward to developing ties with Hungary and Visegrad Group. Will work closely on bilateral cooperation and in the multilateral arena," Jaishankar tweeted.
He had been posted in the 1990s as Counsellor (Commercial) in the Indian mission in Budapest.
The Visegrad Group is a cultural and political alliance of four Central European countries - the Czech Republic, Hungary, Poland and Slovakia, that are members of the European Union and NATO.
A Cultural Exchange Programme between India and Hungary was inked by Jaishankar and Szijjarto.
The two jointly addressed a press conference and replied to questions from the media on wide-ranging issues.
Jaishankar also met Peter Cseresnyes, Chairman of the Indo-Hungarian Parliamentary Society. Both leaders discussed bilateral relations, especially parliamentary exchanges and cooperation.
The EAM also addressed the Hungarian Annual Ambassadors' Conference, Peter Szijjarto followed by a Q & A session.
Earlier, Jaishankar was received at the airport on Sunday by Ambassador Kumar Tuhin and senior officials from the Hungarian side.
India is keen to reinvigorate its ties with the central and eastern European countries. Hungary is also an integral part of the Trans-European Transport Network and located at the crossroads of four trans-European and two European Rail Traffic Management System corridors, thus enabling it access to all parts of Europe.
Budapest could also play an important role in the multi-modal International North-South Transport Corridor (INSTC) project. This would facilitate Hungary and India to be each other's bridge to Asia and Europe respectively.
The EAM's visit is in keeping with the government's priority of boosting ties with smaller nations. It also comes days after Vice President M. Venkaiah Naidu visited the three Baltic countries of Lithuania, Latvia and Estonia from August 17-21, in the first-ever such high-level visit from India.
Naidu's visit came in the backdrop of India's keenness to push the International North-South Transport Corridor project, that aims to link the Indian Ocean with the Baltic Sea, and provide seamless connectivity.
The North-South Transport Corridor project would help Asian and European countries transport their cargo through the Corridor at double speed compared to the Suez canal. It is thought to be the most suitable route for transit traffic between Asia and Europe as only a few countries exist along the route, which means fewer border crossings, and easier for the countries to reach agreements.
( With inputs from IANS )