But just two days after the truce was signed in Minsk, Belarus, calling for "decentralization of power" as the most important step after a halt to the violence, Yuri V. Lutsenko, an influential adviser to Mr. Poroshenko, published an article on Sunday denouncing the idea of creating a special autonomous zone in the east - which Russia has demanded - saying it would be "a cancerous tumor in the Ukrainian organism."
Ukraine Crisis in Maps
Despite Russia's official position that it is not a party to the conflict in eastern Ukraine, the Kremlin has laid out in writing its demands for a new political system in Ukraine, including a new constitution that would turn the country into a federation of largely autonomous regions and enshrine its "neutral military-political status" - precluding membership in NATO.
The Ukrainian government's plan would maintain a strong central government in Kiev and increase the budget authority of local governments while constraining the role of regional governors - a step to prevent the possibility of powerful regional officials with greater loyalty to Moscow.
In addition to the Kremlin's demands that Ukraine not join NATO and that regional autonomy go beyond what the Kyiv government has proposed, political analysts say any agreement between Ukraine and pro-Russian separatists would likely have to include some concessions to Russia regarding a new free trade agreement between Ukraine and the European Union - perhaps establishing a special trade relationship between Russia and eastern Ukraine.
"In terms of a sort of practical relationship, it seems to me those might be the contours of some kind of agreement, which over time could be acceptable to the Ukrainian side," said Adrian Karatnycky, an expert on Ukraine at the Atlantic Council of the United States.
At the moment, with public tensions running high and Ukrainian parliamentary elections seven weeks away, it may be difficult to reach a deal before the cease-fire crumbles.
"Right now, no Ukrainian official will say this is acceptable," Mr. Karatnycky said.
A truce drew basement-dwellers upstairs on Sunday. Credit Mauricio Lima for The New York Times
Alexander Baunov, a Russian writer and political commentator, said the prospects of long-term political agreement seemed extremely remote. "They don't trust each other, and both sides are trying to deceive each other and impose its understanding of the agreement to the rest of the world," Mr. Baunov said.
He said that Mr. Poroshenko appears to be trying to bide time for the government in Kiev to regain control over the region, while Mr. Putin is eager to secure Russia's influence. "The Putin goal is federalization in some way creating an autonomous region inside Ukraine that would influence the whole of Ukraine, in a political way, military way, economic way, binding it with Russia and preventing the whole of Ukraine from going very rapidly to the West without consulting with the Kremlin and with Putin."
Aside from deep mistrust after months of bloody fighting, there are a number of other practical obstacles that make any political agreement extremely difficult to achieve. Among them are Ukraine's parliamentary elections, now scheduled for Oct. 26, which have lawmakers and leaders of the country's major political parties focused on political imperatives to boost their chances at the polls.
"Talk about a bad time to be making massive political compromises," said Samuel Charap, a Russia and Ukraine expert at the International Institute for Strategic Studies in Washington.
Many analysts are deeply skeptical that a deal can be reached before fighting again breaks out.
"They could not vote for changing the Constitution," said Yevgeny Minchenko, a political analyst in Moscow, "because domestic politics in Ukraine is now very radicalized."
Pool photo by Leon Neal
Video: A look at how the threat of further Russian aggression has helped to unify NATO (video credit by Natalia V. Osipova and Christian Roman on Publish Date September 3, 2014 ).
Mr. Minchenko added, "Unfortunately, I am afraid that the point of no return is already passed and we will see a lot more acts of this big drama and of this big civil war."
It is far from clear that the lull in the fighting is sustainable.
Sporadic breaches of the cease-fire between Ukrainian and rebel forces continued Sunday with mortar and gunfire resounding on the northern outskirts of Donetsk, where a contingent of Ukrainian soldiers at the airport is almost surrounded by pro-Russian rebels. Ukrainian troops appeared to be firing from the airport, but there did not seem to be an attack by rebels underway. There had been shelling from heavy artillery by rebel forces overnight Saturday on Ukrainian positions on the edge of the city of Mariupol.
In Kyiv, a military spokesman said that despite the breaches, Ukraine still planned to respect the cease-fire.
The spokesman, Volodymyr Polyovyi, said that the sides had also begun to carry out a prisoner exchange called for in the truce agreement, and that two captured Ukrainian soldiers had been released at a Russian border crossing near Luhansk.
In the center of the Donetsk region, the roads have opened up and people were traveling home, or using the break from hostilities to fetch things they need. Elderly residents and women with young children emerged from a deep bunker under a technical college near Yasinovataya to sit in the sun. Up to 200 people have been staying in the bunker without electricity or running water to escape weeks of heavy bombardment in the town.
"There is no guarantee that it will not start in an hour or two hours," said one woman in slippers and a housecoat, who only gave her first name, Svetlana.
Some analysts in Russia and Ukraine say it remains unclear if Mr. Putin wants a political settlement, and suggest that he may ultimately prefer a continuing conflict that effectively turns eastern Ukraine into a larger, more useful version of other pro-Russian breakaway regions like Transnistria in Moldova or Abkhazia along the border with Georgia.
At the same time, a breakaway Donbass, as eastern Ukraine is known, would also be far more expensive for Moscow to maintain, politically and financially, creating some incentive for a deal, analysts said.
The precise shape of the Ukrainian government is certainly less important to Mr. Putin than protecting Russia's military, strategic and economic interests in eastern Ukraine.
In the demands laid out by its Foreign Ministry in March, Russia also said it wanted direct election of regional parliaments and executive officials, the designation of Russian as an official language in addition to Ukrainian, and official recognition of Crimea's decision to secede from Ukraine.
Many of those demands, particularly the recognition of Crimea as Russian territory, are political nonstarters for many Ukrainians outside of the pro-Russian east. And Russia's proposals for expanding local political control go beyond what the Kiev government had been planning in terms of decentralization.
Many political analysts have argued that decentralizing governmental authority in Ukraine would be a good idea regardless of Russia's interests because it would help the country combat years of dysfunction and corruption in the central government in Kiev. These experts say the Ukrainian Constitution, since independence from the Soviet Union, has granted too much unchecked authority to a series of corrupt and ineffective national leaders.
"These are two separate questions," said Mr. Charap of the International Institute for Strategic Studies. "What Putin would want and what would be good for Ukraine. I don't know that a decentralization plan that would be good for Ukraine would be enough for him."
Mr. Lutsenko, in the article in Ukrainska Pravda, said the only hope for Ukraine was to push closer to Europe, fight corruption and stave off Russian influence. "And when our living standard will be attractive even for Kremlin-poisoned Donbass citizens," he wrote, "we will open the doors to all who recognize the integral, unitary European Ukraine."
Carlotta Gall contributed reporting from Yasinovataya, Ukraine, and Neil MacFarquhar from Kyiv, Ukraine.