“The Ukrainian people and government have embarked on an effort today to reclaim one city in the eastern part of their country,” she said. “Their response is reasonable, it is proportional, and frankly it is what any one of our countries would have done in the face of this threat.”

The Ukrainian army units in Slovyansk did not seem eager to engage the militants fully, and appeared to limit their activities for the day to tightening a cordon around the militant stronghold. The city’s center remained under the control of antigovernment militias, who manned barricades as streets fell nearly silent ahead of what residents feared could become a general assault.

“They are coming at us from all sides,” said one fighter in camouflage and sneakers, who gave his name as Sergei, and who held a Kalashnikov assault rifle and said he was a veteran of the Soviet Army.

Both the government and the separatist forces said two helicopters were brought down in the fighting, with at least one crew member killed. These reports could not be verified, and hours later the wreckage had not been found by independent observers.

Late at night, the Ukrainian government said two members of an airborne brigade had been killed, apparently in the brief but intense evening clash at the bridge, which by day had been held by airborne troops.

Earlier, as the first round of fighting died down, Ukrainian troops were posted at their newly captured positions in the villages of Bylbasovka and Andreyevka on the city’s perimeter, where residents flocked to argue with them and urge them not to fight.

In Bylbasovka, a Ukrainian serviceman who identified himself as a staff officer for one of the battalions participating in the operation stood with troops facing about 75 angry residents who demanded that they leave.