Swaraj will call on Conte and also meet her counterpart Enzo Moavero Milanesi.
The external affairs minister will then visit France from June 18-19.
In Paris, Swaraj will meet her counterpart Jean-Yves Le Drian during which both the sides will review the bilateral relations.
India and France are celebrating the 20th anniversary of their Strategic Partnership.
Swaraj will be visiting Luxembourg from June 19-20 and it will be the first ever visit to Luxembourg by an external affairs minister from India, the MEA said.
During her visit, Swaraj will be calling on Grand Duke of Luxembourg Henri Albert Gabriel Flix Marie Guillaume and Prime Minister Xavier Bettel.
"Swaraj will also have meetings with Jean Asselborn, Minister of Foreign and European Affairs and Pierre Gramegna, the Minister of Finance. In Luxembourg, she will also interact with the Indian community," the MEA said.
On the last leg of her tour, Swaraj will visit Belgium from June 20-23.
In Brussels, she will meet Deputy Prime Minister and Minister of Foreign Affairs of Belgium Didier Reynders.
She will also meet President of the European Commission Jean-Claude Juncker and the President of the European Parliament Antonio Tajani.
The MEA said Swaraj will also meet her counterpart Federica Mogherini, the High Representative of the European Union for Foreign Affairs and Security Policy, to review the entire gamut of the India-EU relations.
She will also deliver a keynote speech at the high-level event Climate, Peace and Security: Time for Action', she will lead the International Yoga Day (IYD) celebrations at the European Parliament and also interact with the Indian community, the MEA said.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)