Despite the government's desire to minimize civilian casualties, Ukraine's forces could find themselves dragged into grueling warfare inside the cities in their battle to hold the country together.
"To respond to this phase ... we evidently must change tactics," said Valeriy Chaly, deputy head of the presidential administration. He refrained from specifying how.
Insurgents in Donetsk appeared be bracing for a bitter fight as they shipped their relatives out of the city.
One fighter, who declined to give his name, told The Associated Press that not having his wife and young daughter with him would free him to concentrate on the battles ahead.
"It is easier for us this way. It is easier to fight. Your soul is not ripped into two, because when they're here, you think about war and about your family — if they are OK or not," he said. "When you know that they are safe, it is easier to go to fight."
Meanwhile, the U.S. and the 28-nation European Union separately announced tougher new sanctions against Russia, which is accused of fomenting the unrest by supplying the separatists with fighters and heavy weapons — an allegation Moscow denies.
The U.S. slapped restrictions on Russian weapons manufacturers, energy companies and banks, while the EU moved to stop new European financing agreements with Moscow.
At the same time, the Pentagon warned that Russia is building up its forces along the Ukraine border again, with 12,000 troops massed there, reflecting a steady increase in recent weeks.
If Ukrainian forces take the fight into the heart of rebel-held cities, it will be a type of combat for which they are not believed to be adequately prepared.
"It's a very complicated strategic task — not only when it comes to tactics, also in terms of equipment. When rebels are putting missile launchers on school rooftops, what do you do?" said Orysia Lutsevych, a research fellow at Chatham House in London.
Matthew Clements, an analyst with security affairs consultancy HIS, said Ukraine may, instead of entering Donetsk and Luhansk, surround the cities, "cut the separatists off from supplies of fighters and equipment, and undertake gradual operations against the cities and suburbs in an effort to wear the separatists down."
Disrupting supply lines is a particular priority for Kiev as the rebels have lately come into possession of advanced weapons, including tanks and multiple rocket launchers.
A hail of rockets that Ukrainian officials said came from a Russian-made launcher killed at least 19 government servicemen last week.
Associated Press writers Julie Pace and Matthew Lee in Washington; Mstyslav Chernov in Donetsk, Ukraine; and Matthew Knight in London contributed to this report.