Prime Minister Narendra Modi of India visited Kyiv on Friday, furthering a diplomatic effort by Ukraine to engage non-Western nations in potential settlement talks with Russia, even as Ukraine’s military pressed ahead with an offensive into Russian territory.

Ukraine has been pursuing parallel tracks of seeking international backing for its plans for peace talks while capturing Russian territory that Ukrainian officials say could provide leverage in negotiations, if the ground can be held long enough (a notion that President Vladimir V. Putin of Russia has tried to dispel).

The diplomacy has focused on outreach to India and China, exploring possible roles for the countries in settlement talks.

Mr. Modi’s visit is a first by an Indian leader since Ukraine gained independence in 1991. It is the highest-profile wartime visit of a leader of a nation with a neutral stance on the conflict, and leaders in Kyiv have been trumpeting it as a show of diplomatic support for Ukraine and a potentially positive sign for advancing settlement negotiations.

In Kyiv on Friday, President Volodymyr Zelensky of Ukraine greeted Mr. Modi with a hug and the two leaders lay flowers at a memorial for children killed in the war.

In a joint statement, the leaders indicated they had raised their views on various topics with each other. Mr. Zelensky broached the issue of India’s purchases of Russian oil, which helps fund Moscow’s war effort, but reached no immediate agreements. Mr. Modi expressed support for a move toward settlement talks that involve Russia.

“The Indian side reiterated its principled position and focus on peaceful resolution through dialogue and diplomacy,” the statement said. It noted that, “Prime Minister Modi reiterated the need for sincere and practical engagement between all stakeholders.”

Earlier in the day, Mr. Modi visited a memorial in Kyiv to Gandhi, underscoring the focus on peace.

In Washington, the White House welcomed Mr. Modi’s visit.

“If that can be helpful to getting us to an end to the conflict that comports with President Zelensky’s vision for a just peace, well then, we think that would be helpful,” John F. Kirby, a White House national security spokesman, told reporters.

Mr. Modi has carefully calibrated his country’s relations with the two warring nations. On a trip to Moscow last month, Mr. Modi hugged President Putin, and India has remained an important trading partner with Russia.

India sent a representative to a Ukrainian-organized peace summit in June that Kyiv hoped would win backing for its negotiating positions in potential talks. But India did not join the nations that signed a communiqué at the end of the summit supporting three points of the Ukrainian plan.

Russia was not invited to those talks, and Indian officials have taken the position that their country will not endorse negotiations that do not involve the two warring parties.

Still, India is seen as interested in a settlement to avoid further isolation of Russia that could push Moscow into a tighter embrace with China, India’s rival in Asia. India relies on Russian weaponry for its military and, during the war in Ukraine, has purchased discounted oil from Russian companies that have been placed under sanctions by the United States and Europe.

Mr. Zelensky said last month that Russia could be invited to talks by the end of the year. In the statement on Friday, Ukraine again raised the possibility for engagement with Russia, saying its diplomacy could include “peace based on dialogue.”

Ukraine’s plan lays out 10 points for negotiation, including payment of reparations for war damage and prosecutions of war crimes. But at the June summit in Switzerland, Ukraine was forced to scale back its framework to three points, because most attendees would not sign on to a broader framework.

India’s Minister of External Affairs, Subrahmanyam Jaishankar, told a news conference in Kyiv on Friday that the two leaders had a “very back and forth discussion.” India, he said, had conveyed an offer to assist in talks. “We are willing to do whatever we can,” he said, “because we do think that the continuation of this conflict is terrible, obviously for Ukraine itself but for the world as well.”

Mr. Modi’s visit to Kyiv coincided with a Ukrainian military incursion into Russia that officials in Kyiv say is intended to give them leverage in possible talks and divert Russian forces that have been attacking inside Ukraine. President Vladimir V. Putin of Russia has rebuffed the idea, saying he won’t negotiate while Ukrainian troops are on Russian soil.

The strategy is fraught with risks: For the operation, Ukraine pulled troops from defensive positions inside the country. Those positions are now under attack by Russian troops moving relentlessly forward.

Ukraine has courted support for its negotiating plan from developing nations by pointing at the war’s risks to grain exports over the Black Sea; earlier in the conflict, a Russian blockade of grain shipments caused a spike in global food prices. Ukraine has also argued that any settlement shifting borders would set a precedent endangering stability in Asia, Africa and South America.

Ukraine’s interests lie in winning diplomatic backing for its negotiating positions from as broad an international coalition as possible. The visit by Mr. Modi, though he did not endorse the Ukrainian initiative, helps to signal non-Western support for settlement talks that take into account Kyiv’s interests, Ukraine’s foreign minister, Dmytro Kuleba, said in an interview on Thursday.

“Russia’s main narrative is this is a war of the West against the rest,” Mr. Kuleba said. “Everything that has been happening over the course of the past months defies this argument. This is a strategic line that we have pursued from the very beginning.”

He said he presumed that Mr. Putin would be “very upset” by Mr. Modi’s visit.

For Mr. Modi, the Kyiv visit is “about positioning India as a voice of the global south” on the war in Ukraine, Harsh V. Pant, a professor of international relations at King’s College London, said in an interview. He added that the trip created a chance “to talk about, in some ways, the impact this conflict has had” on poorer nations.

Mr. Modi arrived, as other foreign dignitaries have, by train to Ukraine’s capital, where flights have been grounded as too dangerous since Russia’s all-out invasion two-and-a-half years ago.

Suhasini Raj contributed reporting from New Delhi and Stas Kozljuk from Kyiv, Ukraine. Eric Schmitt contributed from Washington, D.C.