MOSCOW, Jul. 9 (Reuters) - Indian Prime Minister Narendra Modi told Russian President Vladimir Putin on Tuesday that the death of innocent children was painful and terrifying, a day after a lethal strike on a children's hospital in the Ukrainian capital Kyiv.

The visiting Indian leader used emotive language to deliver an implicit rebuke to Putin at a summit intended to underscore the deepening partnership between their two countries.

Winding up his two-day trip, the two sides set out nine key areas for closer cooperation, ranging from nuclear energy to medicine, and said they aimed to boost bilateral trade by more than half to hit $100 billion by 2030.

But given that Putin has rarely been publicly criticised face-to-face over the war in Ukraine by the leader of a country that Russia sees as a friend, Modi's televised comments were striking.

"Whether it is war, conflict or a terrorist attack, any person who believes in humanity is pained when there is loss of lives," Modi said.

"But even in that, when innocent children are killed, the heart bleeds and that pain is very terrifying."

Ukraine says it has recovered fragments of a Russian Kh-101 cruise missile at the Kyiv children's hospital which was hit on Monday during a wave of Russian attacks that killed 44 Ukrainians, including four children, across the country.

At the hospital itself, two adults were killed and Interfax Ukraine said eight children were among about 50 people wounded.

Russia said, without providing evidence, that it was a Ukrainian anti-missile system that struck the hospital.

Modi appeared to criticise Russia once before over its actions in Ukraine when he told Putin in September 2022 that "today's era is not an era of war". Putin said at that time he understood Modi's concerns.

India, however, has not condemned Russia's invasion and has taken the opportunity to buy record amounts of discounted Russian oil as sanctions have decimated Moscow's trade with the West.

Indian Foreign Secretary Vinay Mohan Kwatra, accompanying Modi on the trip, said India wanted to further strengthen energy ties and could seek deals with Rosneft (ROSN.MM) and other leading Russian oil firms. The two countries said they were also exploring an increase in Russian coal sales to India.

In joint statements, they further outlined plans for closer cooperation in developing the Northern Sea Route through Arctic waters and for working together in space exploration, among other areas.

Photo from Reuters