NEW YORK / WASHINGTON / MOSCOW / PARIS - US President Donald Trump said Tuesday that the United States will help defend Ukraine after its war with Russia, but that there will not be US troops on the ground.

"You have my assurance," Trump said in a Fox News interview, a day after hosting a White House summit with Ukrainian President Volodymyr Zelensky and other European leaders.

Trump said on Monday during meetings at the White House that the United States would be "involved" in security guarantees for Ukraine after its war with Russia but did not elaborate. He added more clarity in the morning interview with Fox & Friends.

"When it comes to security, they're willing to put people on the ground," Trump said, referring to the European countries.

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"We're willing to help them with things, especially probably ... by air because there's nobody that has the kind of stuff we have."

"The issue of security guarantees for Ukraine -- and potential US involvement in them -- has proved to be a sticking point as Trump works to broker peace between Ukraine and Russia," reported The Washington Post about the development.

"European leaders have been encouraged that Trump appears open to a US role in peacekeeping in Ukraine, but that could complicate negotiations with Russia, which has spent years working to counter increased military support for Ukraine by its allies," it noted.

The White House rarely hosts so many foreign dignitaries at once as it did on Monday, when Zelensky and European leaders arrived to discuss the Russia-Ukraine conflict with Trump.

The Monday meetings at the White House mainly focused on security guarantees for Ukraine and a possible trilateral meeting between Russia, Ukraine and the United States. Disagreements remain on some key issues, such as whether a ceasefire is necessary before further negotiations.

The latest talks came three days after the US and Russian presidents met in the US state of Alaska, when progress was reportedly made but no deal was announced.

READ MORE: Trump meets Zelensky, European leaders on resolving Ukrainian crisis

Guarantees for peace in Ukraine

Trump has directed his team to come up with a framework for security guarantees that will help ensure lasting peace in Ukraine, White House press secretary Karoline Leavitt said Tuesday.

The accommodations of a potential Putin-Zelensky meeting are on the way, and both sides expressed willingness for talks, she told a press briefing.

He again categorically ruled out Ukraine joining the North Atlantic Treaty Organization (NATO).

While security guarantees remain a key Ukrainian demand, Russia's Ministry of Foreign Affairs said it rejects any scenario involving the deployment of NATO troops in Ukraine, warning such a move could trigger an uncontrollable escalation with unpredictable consequences.

Resolving the conflict 

Russia does not reject any formats, either bilateral or trilateral, on resolving the conflict in Ukraine, Russian Foreign Minister Sergei Lavrov said Tuesday.

Speaking on state TV's Rossiya-24 channel, he also noted that any contacts over Ukraine involving top officials need to be prepared "extremely carefully."

READ MORE: Trump: Zelensky can end conflict, but NATO bid, Crimea off limits

The foreign minister added that there can be no talk of any long-term agreements without respect for Russia's security and the rights of Russians in Ukraine.

Putin-Zelensky meeting

On Monday night, Trump said in a post on the Truth Social platform that he had called Putin and began arranging a bilateral meeting between Putin and Zelensky, with the location to be determined.

Trump added that after a Putin-Zelensky meeting, a trilateral meeting involving US, Russian and Ukrainian leaders would take place.

French President Emmanuel Macron said on Tuesday that a meeting between Putin and Zelensky could happen in the next two weeks.

Speaking in an interview with the LCI news channel, Macron said that Putin expressed his readiness to meet Zelensky within that timeframe.

"We have decided to have a bilateral meeting between the two presidents, then a trilateral meeting (with Trump), and then a multilateral meeting where the Europeans must be at the table," Macron said.

The French president added that such meetings should be held in Europe, reflecting the "collective will" of European leaders.

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Unlike their 2019 meeting in France, Macron suggested that the upcoming meetings could take place in a "neutral country," such as Switzerland or Turkiye, where Russia and Ukraine have previously held bilateral talks.

Bodies of fallen soldiers 

Meanwhile, Russia and Ukraine on Tuesday exchanged more bodies of fallen soldiers under the Istanbul deal, Russian presidential aide Vladimir Medinsky said.

Moscow had handed over 1,000 bodies of fallen soldiers to Kyiv, while Ukraine had transferred 19 bodies to Russia, said Medinsky, also Russia's chief negotiator at the talks with the Ukrainian side.

During their second round of talks on June 2 in Istanbul, Russia and Ukraine agreed on an "all-for-all" exchange of seriously ill and wounded prisoners, and soldiers under the age of 25, as well as the transfer of bodies of fallen soldiers.

On July 23, after the last round of Russia-Ukraine direct talks, Medinsky said Russia had returned the bodies of 7,000 fallen Ukrainian soldiers and was ready to return 3,000 more.  

Russia strikes Ukrainian oil refinery

Also on Tuesday, Russian forces conducted a group strike on a Ukrainian oil refinery supplying fuel to the Ukrainian troops in the Donbass region, the Russian Defense Ministry said.

The raid involved long-range precision weapons, as well as combat drones, the ministry said in a statement.

It added that the strike had achieved its goal and designated targets were hit.