In the call to Putin, Obama reiterated US support for Ukraine's sovereignty and emphasised the importance of reaching a diplomatic resolution.
"However, if Russia continues its aggressive actions in Ukraine, including by sending troops, weapons, and financing to support the separatists, the costs for Russia will rise," the White House said in a statement.
The Ukrainian leader's office said Poroshenko and Obama expressed hope that today's summit would bring a halt to fighting.
Poroshenko said the "meeting in Minsk offers one of the last chances to declare an unconditional ceasefire and pull back heavy artillery".
Russia, however, is likely to get even more concessions. Details suggest the proposal is a hasty remake of last September's failed ceasefire package: a truce and a buffer zone that would effectively consolidate the rebels' advance.
Compared with the burst of optimism that met the first ceasefire plan, scepticism in the West now runs deep.
German Chancellor Angela Merkel and French President Francois Hollande are gloomy, and refuse to talk up prospects of a deal. The United States is mulling plans to beef up weapons shipments to Kiev, a move opposed by Merkel and others. Both the European and American threats are being put on hold to try to gain the maximum leverage in the tentative peace talks.
Klaus Segbers, an analyst at the Centre for Global Politics at Berlin's Free University, told the Herald he doubted the Minsk talks could throw Putin off track.
"The Ukrainian Government doesn't have assets to put on the table for keeping their country intact," Segbers said.
"Merkel and Hollande will try to prevent an intensification of the civil war in their neighbourhood, but don't have much to offer. For the Ukrainians, neither the European Union nor Nato membership will be offered. For the Russians, there aren't positive incentives to get out of there, and no real threats beyond existing sanctions. Military options won't be considered."
The Kremlin's goal, Finnish President Sauli Niinisto said, is "to keep Ukraine unstable, and waiting maybe a possibility if something opens to do something new".
British Foreign Secretary Phil Hammond accused Putin of acting "like some mid-20th century tyrant". President Dalia Grybauskaite of Lithuania, one of the trio of Baltic states that bolted from the Soviet Union when the Cold War ended, warned that failure to stand up to Putin now would simply sharpen his appetite for more. "After Ukraine, we will be next."
Russia analysts say Putin - initially hailed as open and friendly when he became President in 2000 - seems more and more persuaded to renounce the post-Cold War order.
In his view, the end of the Cold War left Russia diminished and the United States installed as the sole superpower. It allowed Nato to expand up to the Russian borders. And, in Putin's thinking, it lured Russia into the globalised economy, making it vulnerable to external pressures.
US hegemony is a "pseudo-occupation, but we won't put up with it", Putin said at the weekend.
If this analysis is right, Putin has torn up the rulebook for peaceful co-existence written after the collapse of the Soviet Union. But the matrix of the Cold War is not the same as the situation today, Bobo Lo, a former Australian diplomat in Moscow and author of Russia and the New World Disorder, told the Herald.
Compared to the Soviet Union 50 years ago, Russia in 2015 is no match for America in terms of military might, political influence and, especially, economic power. Dependent on foreign investment and energy exports, Russia is starting to hurt as a result of the impact of Western sanctions and the oil price fall.
"In the Cold War, the US and the Soviet Union kind of knew how they were going to act. People could read a given situation," Lo said.
"That is not the case now - we lack those checks and balances, we lack that predictability."
