US President Donald Trump said that Russia and Ukraine would immediately start ceasefire talks after he spoke with Russian counterpart Vladimir Putin Monday, but the Kremlin leader fell short of agreeing to the unconditional truce proposed by Washington. Trump painted a more upbeat picture of the situation after the two-hour call, as he desperately seeks a deal to end a grinding conflict that he had promised on the election trail to solve within 24 hours. Putin said he was ready to work with Kyiv on a memorandum towards a possible peace deal after the "useful" call -- but insisted that more compromises were necessary to end the war Moscow launched in February 2022. "Just completed my two-hour call with President Vladimir Putin of Russia. I believe it went very well," Trump said on his Truth Social network. "Russia and Ukraine will immediately start negotiations toward a Ceasefire and, more importantly, an END to the War." Trump added that the "tone and spirit of the conversation were excellent," after the US president had shown signs of increasing frustration with the Kremlin leader. Trump recently called for a 30-day unconditional ceasefire between Ukraine and Russia. Kyiv agreed, but Putin has so far held off on any such truce. The Vatican -- where Pope Leo XIV was recently elected as the first American pontiff -- would be "very interested" in hosting the Russia-Ukraine talks, Trump added. Putin was more circumspect, even as he appeared to give one of the most concrete signs yet of being ready to discuss an end to Moscow's invasion of its neighbor. "It was very informative and very open and overall, in my opinion, very useful," Putin told Russian media after the call. He said that Russia would "propose and will be ready to work with the Ukrainian side on a memorandum on a possible future peace agreement defining a range of positions." His comments left many details unclear, however, including on the timing and contents of the document. The Russian president added that while talks with Kyiv last week in Istanbul had put the world "on the right path" to resolving the conflict, more "compromises" were still needed. The US president briefly spoke to Zelensky before Putin, with the Ukrainian leader urging him to toughen sanctions against Russia if it did not agree to a ceasefire. Trump added that he had "informed" Zelensky, European Commission President Ursula von Der Leyen and the leaders of France, Germany, Italy and Finland of the resumption of peace talks in a call immediately after his conversation with Putin. Germany said after the Trump-Putin call that key European allies of Ukraine had agreed to "increase pressure" on Russia with sanctions. But there were signs from Trump that he is more interested in resetting relations with Moscow than imposing sanctions. He held out the carrot that Russia could do "largescale TRADE with the United States when this catastrophic 'bloodbath' is over." The Kremlin said that both Putin and Trump wanted the "normalization" of US-Russia ties. Still, Trump's frustrations could yet boil over with either side if they fail to reach a deal. US Vice President JD Vance earlier said that if Russia proved unwilling to reach peace "then we're eventually just going to have to say, this is not our war." The White House had earlier said that Trump still hoped to meet Putin in person, after the Russian leader rebuffed his suggestion to meet at last week's Russia-Ukraine talks in Istanbul. On the ground, the Russian army continued its attacks.