The Kremlin, in its own account of the conversation, made clear that Moscow would indeed send help to largely Russian-speaking eastern Ukraine.
"It was noted that the Russian side, in collaboration with representatives of the International Committee of the Red Cross, is sending an aid convoy to Ukraine," the Kremlin statement said, without saying when the convoy was going.
U.N. agencies say more than 1,100 people have been killed including government forces, rebels and civilians in the four months since rebels seized territory in the east and Kiev launched its crackdown.
Ukrainian President Petro Poroshenko said he supported an aid mission but made clear it had to be an international effort under the aegis of the Red Cross, involving the European Union as well as Russia. Poroshenko said U.S. President Barack Obama had also backed the international plan when they spoke on the telephone on Monday.
The International Committee of the Red Cross made no immediate comment, although last weekend it issued a statement acknowledging receipt of an offer from Russian Foreign Minister Sergei Lavrov about organizing aid convoys. The past week has seen increasingly urgent warnings from Kiev and Western countries that Moscow appeared to be planning an invasion. Western countries say Putin - who has whipped up the passions of Russians with a relentless nationalist campaign in state-controlled media since annexing Ukraine's Crimea peninsula in March - could invade to head off a humiliating rebel defeat.
Kiev said it was in the "final stages" of recapturing the eastern city of Donetsk - the main base of the separatist rebels - in a battle that could mark a turning point in a conflict that has caused the biggest confrontation between Russia and the West since the Cold War. An industrial metropolis with a pre-war population of nearly 1 million, Donetsk rocked to the crash of shells and gunfire over the weekend, and heavy guns boomed through the night into Monday from the outskirts of the city.
NATO Secretary-General Anders Fogh Rasmussen said there was no sign Russia had withdrawn the troops it had massed at the Ukrainian frontier. Asked in a Reuters interview how he rated the chances of Russian military intervention, Rasmussen said: "There is a high probability."
"We see the Russians developing the narrative and the pretext for such an operation under the guise of a humanitarian operation, and we see a military build-up that could be used to conduct such illegal military operations in Ukraine," he said.