Delhi's top diplomat was the guest of honour as EU foreign ministers met in Brussels with an eye to renewing relations and boosting trade with the south Asian giant.
EU president Ursula von der Leyen's new Commission wants to give Brussels a more "geopolitical role" and as part of that hopes to host a March summit with powerful Indian leader Prime Minister Narendra Modi.
"India and the European Union share a lot of things," said Europe's high representative for foreign policy Josep Borrell, citing climate change, the digital revolution and rise of China as shared challenges.
Jaishankar, standing by Borrell, noted that the new government in India and the new commission in Brussels are "both quite fresh" and that they hoped to take relations to a "new level".
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He said he hoped the lunch talks would confirm the "strategic partnership."
Taken together, the EU member states are Delhi's biggest trade partner, with India's imports and exports to and from the bloc each representing about $49 billion.
But, while Europe has inked trade deals with big Asian players Japan, Vietnam and Singapore, the pair have no formal agreement, and India approaches such agreements carefully.
"You don't necessarily need trade deals to do trade," Jaishankar told AFP, stressing that India's economy is driven by domestic demand.
"Trade deals are useful, I mean I'm not at all denying that, but I think they are not necessarily as compelling as sometimes all of us tend to think."
European business wants to win more access to markets in a country with 1.4 billion people, and Jaishankar was clear that Delhi would like closer cooperation with Europe on security and strategic policy.
But some in Europe are worried about what they see as India's populist shift under Modi's right-wing government.
Lawmakers in the European Parliament have drafted a resolution condemning India's Citizenship Amendment Act of 2019 as "discriminatory in nature and dangerously divisive."
But the non-binding resolution has yet to be passed and Jaishankar insisted the law had been misunderstood.
The CAA laws eases citizenship rules for religious minorities such as Hindus and Christians from Muslim-majority Bangladesh, Pakistan and Afghanistan.
Protests have erupted in India, and concerns have been raised abroad, led by those who fear the Hindu nationalist government is discriminating against Muslims and putting secularism in danger.
But Jaishankar said Delhi's critics have misunderstood the government's policy and been taken in by the politics of a "very passionate" democratic society.
He compared the CAA rules to immigration and refugee resettlement policies across Europe, pointing out that many EU countries also use national or cultural criteria.
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"They created pathways to naturalisation to citizenship," he said, citing among others Germany's rule allowing ethnic Germans from eastern Europe to seek citizenship.
"Now, they did it with a context and they did it with a criteria. I mean, no European country said: 'Anybody anytime, anywhere in the world can come because they feel it's nice to live in Europe'."
Without mentioning Pakistan by name, he said some of India's neighbours have Islam as a state religion, "and there are persecuted religious minorities who came to India because many of them find people have the same faith."
He said India's new law would reduce statelessness, and pointed to the fierce debates that Europe has also had around immigrations and the "political changes" these have caused.
Modi's government also raised eyebrows in Brussels when it stripped Indian Kashmir of its partial autonomy and imposed a security crackdown in its only Muslim-majority region.
Indian invited international ambassadors to tour the region last week and Jaishankar was keen to stress that, alongside the political dispute, the government is investing there.
"Kashmir in its social economic outlook was less and less aligned with the rest of India because the rest of India is moving in a very progressive direction," he said.
Jaishankar reeled off a list of projects in Kashmir, including the electrification of 330,000 homes and increasing pension and benefits coverage from 62 to 80 per cent of the population.
Seven medical colleges are "in the pipeline" and three frozen hydroelectric projects have been unfrozen.
"It's our case that Jammu and Kashmir is moving in the right direction but we also have been honest enough in saying that, well, there are there are challenges still ahead," he said.
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