BELGOROD, Russia — On the outskirts of this sleepy city bordering Ukraine, residents were surprised Thursday when a military helicopter lifted off into the dreary sky.

“Look! They brought out the real machines today,” said Viktor Naumov, 28, a courier, who pulled his car over to the shoulder of an adjacent highway to give a shout of appreciation.

The helicopter was one of the few visible signs here of what Western governments, including the United States, say is a muster of tens of thousands of troops deployed by the Kremlin that could preface an invasion of Ukraine, a step that President Vladimir V. Putin has said he might employ to protect Russian-speakers in the country’s east.

But in and around Belgorod, which sits a scant 40 miles from Kharkiv, Ukraine’s second-largest city and a likely target in case of an invasion, any increased military presence is largely kept out of the public eye. In a region that appears far from being on the brink of war, life continues as normal here, and many residents say they do not want war, dismissing reports of a buildup as rumors set to discredit Russia.