Fierce fighting raged inside Russia on Thursday after Ukrainian armored columns reportedly advanced as far as six miles into Russian territory and captured several small settlements.

The incursion, which was filmed on videos posted online and reported by Russian officials and military analysts, prompted the local governor to declare a state of emergency. On Wednesday President Vladimir V. Putin of Russia convened with top military and security officials to strategize about the attack.

The surprising assault appears to represent an effort by Ukraine to turn the tables on Moscow by pushing into its territory. In May, Russia caught Ukraine off guard when it sent troops across the border in the area north of Kharkiv, where it still has a narrow foothold.

Ukraine has remained mostly silent about the attack, which began on Tuesday. The Ukrainian military has not acknowledged its troops are in Russia.

The incursion is the third significant Ukrainian ground assault on Russian territory since the start of the full-scale invasion of Ukraine more than two years ago. But it appears to be the largest, according to open-source intelligence analysts studying photographs and videos from the area of Russia under attack, a rolling expanse of farm fields, forests and small towns.

Some analysts estimate that Ukraine has sent hundreds of troops into Russia. That would be a major commitment at a time when Ukrainian forces are under heavy pressure along the front lines in the south and east of their country.