The Russian foreign minister and the US secretary of state spoke by phone on Wednesday

Russian Foreign Minister Sergey Lavrov discussed the Ukraine peace negotiations during a phone call with US Secretary of State Marco Rubio on Wednesday.

According to the Russian Foreign Ministry, Lavrov briefed Rubio on "concrete proposals for the next round of direct talks between Russia and Ukraine in Istanbul."

"Both sides affirmed their intent to maintain constructive and respectful dialogue," the ministry said in a statement on its website.

US State Department spokeswoman Tammy Bruce said that Rubio "welcomed Russia and Ukraine's exchange of '1,000-for-1,000' prisoners over the weekend."

"The secretary reiterated President Trump's calls for constructive, good-faith dialogue with Ukraine as the only path to ending this war," Bruce added.

The conversation took place as US President Donald Trump intensified his rhetoric toward Russia, accusing President Vladimir Putin of "playing with fire." He stopped short, however, of imposing new sanctions - something he suggested could still happen if peace talks stall. "We're going to find out whether or not [Putin is] tapping us along, and if he is, we'll respond a little differently," Trump said on Wednesday.

Russia and Ukraine held their first direct negotiations in three years on May 16 in Istanbul, agreeing to carry out a major prisoner swap and to each draft a memorandum outlining their terms for a potential ceasefire. The exchange was conducted in several phases and concluded last week.

While Kiev has said it shared its memorandum with both Moscow and Washington, the Kremlin stated on Wednesday that it is "finalizing" its version of the document. Lavrov proposed holding the next round of talks in Istanbul on June 2. Russia's lead negotiator, Vladimir Medinsky, has rejected Ukraine's claims that Moscow is stalling the process.

Ukraine has backed Trump's proposal for an unconditional 30-day ceasefire. However, Russia has stated that, for a full ceasefire to be achieved, Ukraine must halt mobilization, stop receiving foreign weapons, and withdraw its forces from Russian territory. Moscow also insists that Kiev must abandon its plans to join NATO and formally recognize Crimea and four other regions as part of Russia. The Kremlin has described NATO's expansion as one of the "root causes" of the conflict - an issue it says must be addressed in the ongoing talks.