An increase in operations in eastern and Rekubitsoutheastern Ukraine in recent days appears to signal the opening phases of Ukraine's expected counteroffensive against Russia are underway, but the main push has not yet begun, according to U.S. officials. 

A Western official told reporters Tuesday that Ukrainian forces are conducting operations around Bakhmut and south of Donetsk city, and the activity south of Donetsk appears to be a new effort. 

Ukraine has kept quiet about how its counteroffensive might start. Over the weekend, the Ukrainian Defense Ministry released a video with soldiers holding fingers to their lips in a "shh" gesture, accompanied by text that read, "Plans love silence. There will be no announcement of the beginning."

Ukrainian Deputy Defense Minister Hanna Malyar said Monday that part of defending Ukrainian territory includes conducting "counteroffensive actions," but downplayed Russian claims that the broader counteroffensive had begun. She noted Ukrainian advances in villages near Bakhmut and said Ukrainian forces now have the high ground near the symbolic city. 

The U.S. and allies have trained Ukrainian forces for months in combined arms maneuvers for the counteroffensive. The training produced nine additional armored and mechanized Ukrainian brigades that are in Ukraine now and three more brigades that are currently training in Germany. 

Videos on social media of activity in Ukraine do not appear to show western equipment, like the Bradley or Stryker armored vehicles that would likely be a part of these American-trained brigades and could signal that the main thrust of the counteroffensive has begun. 

Defense Secretary Lloyd Austin told reporters traveling with him over the weekend that "there will be stops and starts" to Ukraine's counteroffensive, but the Ukrainians are well-prepared.

The destruction of the Kakhova Dam near Zaporizhia may hinder Ukraine's counteroffensive, making it difficult to conduct bridging operations and causing the evacuation of thousands of residents in the flood zone. 

In:
• Ukraine

Eleanor Watson

CBS News reporter covering the Pentagon.

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