Russian President Vladimir Putin and Austrian Chancellor Karl Nehammer started negotiations Monday in the Russian presidential residence, Russia's semi-official Interfax reported, citing Kremlin spokesperson Dmitry Peskov.

This marked the first visit to Russia by an EU leader since the invasion started.

After the meeting Nehammer told reporters this wasn't a "friendly visit" with Putin and that he addressed the "serious war crimes in Bucha," The Austrian Press Agency reported. Nehammer said he told the Russian leader that the sanctions will escalate if Ukrainians keep dying, according to The Austrian Press Agency.

At a virtual meeting on Monday, President Joe Biden and Indian Prime Minister Narendra Modi spoke about Russia's war in Ukraine -- a topic that has caused some friction between the two countries as India has taken a more neutral stance.

Biden said, "I want to welcome India's humanitarian support from people in Ukraine, who are suffering a horrific assault, including a tragic shelling in a train station last week that killed dozens of innocent children and women and civilians attempting to flee the violence. The United States and India are going to continue our close consultation on how to manage the destabilizing effects of this Russian war."

Biden added, "I'm looking forward to our discussion today, Mr. Prime Minister. Our continued consultation and dialogue are key to ensuring the US-India relationship continues to grow deeper and stronger, delivering our people and our global good -- good that we all are seeking to manage particularly in your part of the world."

Modi said the situation in Ukraine was "very worrying," noting he has spoken to both Russian President Vladimir Putin and Ukrainian President Volodymyr Zelenskyy and called for peace and direct talks between the two.

Modi called the killings of civilians in the Ukrainian city of Bucha "very worrying." "We instantly condemned the killings and have called for an independent inquiry. We hope that the ongoing discussions between Russia and Ukraine will lead to peace," Modi said via a translator.

"We have also emphasized the importance of the security of civilians in Ukraine and the unhindered supply of humanitarian assistance to them," he added. "We have sent medicines and other relief material to Ukraine and to its neighboring countries. And on Ukraine's request, we will be sending them another consignment of medicines very soon."

After the leaders' call, a senior administration official told reporters that "there was no sort of concrete ask and concrete answer" on India's response to the war in Ukraine.

Asked about India's purchase of Russian oil during the conflict, the official said energy was brought up on the call but that the U.S. "hasn't asked India to do anything in particular."

"We know not all countries will be able to do what we've done" to ban Russian energy imports, the official said. "Other countries have to make their own choices."

"That said, we don't think India should accelerate or increase the import of Russian energy," the official said.

Asked about India's abstention from the United Nations General Assembly vote to suspend Russia from the U.N. Human Rights Council, the official said, "India is going to make its own judgements."

The official also suggested that India can play a role in mitigating the threat the war has posed to the global food supply, and that there was discussion "about what more India might be able to do."

-ABC News' Molly Nagle and Ben Siegel

Vadym Boychenko, the mayor of the hard-hit Ukrainian city of Mariupol, told The Associated Press that more than 10,000 residents have been killed.

Boychenko said, with corpses "carpeted through the streets," it's possible that the southeastern city's death toll is over 20,000.

-ABC News' Mike Trew

The Ukrainian Armed Forces said Monday that Russian troops are continuing to attack hard-hit Mariupol in southeastern Ukraine.

The Ukrainians said the Russians are still partially blocking the northeast city of Kharkiv using rockets, artillery and mortars.

In Kherson, in the south of Ukraine, Russian forces are trying to gain a foothold in the administrative borders, according to the Ukrainians.

And in Severodonetsk in eastern Ukraine, Russian forces made an unsuccessful attempt to storm the city and weren't able to advance deeper into Ukraine's territory, the Ukrainians said.

-ABC News' Irene Hnatiu

White House national security advisor Jake Sullivan hinted Thursday of more sanctions coming against Russia in the "next week or two" aimed at targeting ways Moscow is evading sanctions already imposed.

“Where our focus will be over the course of the coming days is on evasion,” Sullivan said Thursday at the Economic Club of Washington. “As Russia tries to adjust to the fact that it’s under this massive economic pressure, what steps do they take to try to evade our sanctions and how do we crack down on that? And I think we'll have some announcements in the next week or two that identify targets that are trying to facilitate that evasion both inside Russia and beyond."

When Sullivan was asked whether sanctions will automatically be lifted if a negotiated peace deal between Russia and Ukraine is worked out, he appeared cautious with his words, saying, “a lot of that depends on what the shape and scope” of the agreement is.

“A lot of it depends on what the Ukrainians, in consultation with us and the Europeans come to agree to," Sullivan said. "You know, we're not going to do a deal over the head of the Ukrainians where we give a bunch of sanctions relief to Russia. But if some measure of sanctions relief were built in to some credible diplomatic solution led by the Ukrainians, that's something that we would happily discuss."

But Sullivan said Russian oligarchs shouldn't expect to ever get back their yachts and other assets seized under sanctions that have been imposed, saying the ultimate goal is "not to give them back” once the war is over.

“The president is actively looking at how we can deal with the fact that as we seize these assets, our goal is not to give them back. Our goal is to put them to a better use than that," Sullivan said. "But I'll be careful in what I say today because there's an ongoing kind of policy process around how we end up dealing with that question. But, rest assured, that the goal is not just to sit on them for a while."

-ABC News' Justin Gomez