The main Russian defensive tactic, military analysts have said, is to deploy a thinly manned first line to detect an assault as it is overrun. Behind this line are minefields and then more trenches. Even farther back are reinforcements, which rush forward to counterattack the assaulting troops as they try to cross the minefields.

While the fighting could last for months, both sides are quickly shaping their own narrative of success with vague words and few details.

Sergei K. Shoigu, the Russian defense minister, said that forces of Ukraine’s 47th Mechanized Brigade had tried the breakthrough near Velyka Novosilka. The attack, he said, was repelled.

Other announcements have followed a similar pattern, with unsubstantiated claims of Ukrainian attacks being rebuffed and President Vladimir V. Putin even claiming the counteroffensive so far has failed. The seemingly coordinated Russian messaging on the attacks suggested that the state had prepared for how the counteroffensive would be portrayed, according to the Institute for the Study of War, a U.S.-based analytical group.

The group said that Ukraine was attacking in the three areas but achieving only “differential outcomes” and that seesaw fighting, as assault teams push forward and are beaten back, should be expected.

Ukraine has been even more circumspect, largely staying silent on the fighting. In a rare statement on the offensive, President Volodymyr Zelensky of Ukraine said simply that the Ukrainian military had achieved “step by step” results in fierce battles. And Ukraine has closed media access to the front in Zaporizhzhia region.

Maria Varenikova contributed reporting from Zaporizhzhia, and Eric Schmitt from Washington.