Outright civil war in Ukraine and the division of a country the size of France would have serious implications for countries around, not least for Russia and for NATO states bordering it.
As rebellion simmered, questions were raised about the ability of the army as well as police to confront insurgents.
Police in the eastern port of Mariupol said pro-Russian rebels posing as sympathisers had presented soldiers at a checkpoint with gifts of food.
"It turned out that the food contained a substance that induced sleep among the servicemen," the acting head of Mariupol criminal police department, Alexei Paniotov, said.
"After about half an hour, about 20 unidentified people arrived in three cars and, taking advantage of their helpless state, took them prisoner along with four automatic rifles, a grenade launcher, a machinegun and ammunition."
The five soldiers were freed after negotiations.
Yatseniuk dismissed Russian accusations that his government was provoking bloodshed in the east with an operation to restore Kiev's authority in a series of cities under rebel control.
"The process of dialogue had begun, only it was drowned out by the sound of shooting from automatic rifles of Russian production," he said.
There was renewed diplomatic activity on Sunday.
Russia said it would try to organise talks between Kiev and representatives from the south-east: "It appears that without external help the Kiev authorities are not capable of establishing such a dialogue," Russian deputy foreign minister Grigory Karasin told Rossiya-24 television.
Germany's foreign minister said he was pressing for a second international conference at Geneva to bring Russia and Ukraine together with the United States and European Union to settle the dispute. Moscow and Kiev accuse each other of wrecking a four-way accord to end the conflict signed at Geneva on April 17.
Russian President Vladimir Putin and German Chancellor Angela Merkel discussed the Ukraine crisis in a telephone call and stressed the importance of "effective international action" to reduce tension, the Kremlin said on Sunday.
Read MoreDozens dead asviolence spreads in Ukraine
A German government spokeswoman said they had also discussed a visit to Moscow on Wednesday by the head of the OSCE, the European security body which has been trying to mediate on the ground but saw some of its monitors held for a week by rebels.
Ukraine is divided between a largely Russian-speaking population in the industrial east and Ukrainian-speaking west, where more pro-European Union views prevail. Moscow says Russian-speakers face threats from Ukrainian nationalist militants, an accusation Kiev denies.
There were no signs of Ukrainian forces pushing their declared campaign to remove separatists from eastern cities including Kramatorsk, Donetsk and the rebel stronghold of Slaviansk.
Kiev is organising a presidential election for May 25.
However, as things stand, it would have trouble conducting the vote in many parts of the east, a circumstance that would allow Russia to declare any government emerging as bereft of legitimacy.
Russia denies ambitions to seize eastern Ukraine as it has annexed the Crimea peninsula but reserves the right to send troops to defend Russian-speakers if it deems necessary.
Separatists who have declared a "People's Republic of Donetsk" are planning a referendum on secession next Sunday.
The capital Kiev has remained quiet since the protests that forced Yanukovich to flee to Russia. But celebrations this week marking the anniversary of the Soviet victory in World War Two could be a source of tension.