After a vicious battle for Kharkiv: wreckage, a stuck rocket and artillery booms.

KHARKIV, Ukraine — Ukraine’s military on Friday was waging a fierce battle to push Russian forces back from Ukraine’s second-largest city, Kharkiv, a day after a vicious fight that littered the highway leading into the city with burned-out Russian troop carriers and at least one body.

The troop carriers had been halted at the entrance to the city, in the shadow of huge blue and yellow letters spelling KHARKIV. Nearby, the body of a Russian soldier, dressed in a drab green uniform, lay on the side of the road, dusted in a light coating of snow that fell overnight.

Soldiers sent to hold the position had few details of the fight that took place, saying only that it happened Thursday morning, shortly after Russia’s president, Vladimir V. Putin, gave the order to attack.

“Putin wants us to throw down our weapons,” said a Ukrainian soldier named Andrei, positioned in trench hastily dug into the black mud on the side of the road. “I think we could operate more slyly, gather up our forces and launch a counterattack.”

Off in the distance but close enough to feel, artillery shells boomed. Russian forces, which on Thursday pushed over the border from their staging area near Belgorod, about 40 miles from Kharkiv, have gathered in strength north of the city. It was not clear where or whether they would advance.

Most of the fighting appeared to be taking place a few miles outside the city limits, near a village called Tsyrkuny. The number of military and civilian casualties resulting from the fight were unclear, but on Monday the local police said a 14-year-old boy had been killed in a village near Kharkiv when shell hit near his home. But strikes occasionally hit close enough to the city to elicit shrieks of terror from pedestrians, sending them fleeing into metro stations for cover.

While Russian officials have said their military was endeavoring to avoid civilian areas, the body of a Smerch rocket, which Ukrainian officials said was fired by Russian forces, was stuck vertically in the middle of the street outside the headquarters of the National Guard. A few kilometers away, the rocket’s tail section had buried itself in the asphalt across from an onion-domed Orthodox church.

A team of emergency services officers, dressed in flack jackets and helmets, was attempting to extract the tail from the pavement, but having difficulties. A member of the team said that the tail and the body were different stages of the rocket, likely jettisoned as the explosive ordinance hurtled toward its target near the front lines.

“This is 200 kilos of metal,” the emergency officer said, pointing to the rocket’s tale. “It could have fallen through a building or hit people.”

Even as the artillery barrages intensified, not everyone was ready to hide. Walking with intention toward the source of the artillery booms on the outskirts of Kharkiv was Roman Balakelyev, dressed in camouflage, a double-barreled shotgun slung over his shoulder.

“I live here, this is my home. I’m going to defend it,” said Mr. Balakelyev, who also pulled out a large knife he had strapped to his back as if to show it off. “I don’t think the Russians understand me like I understand them.”

A short while later, Mr. Balakelyev reached the edge of the city, where the Ukrainian troops were huddled around the abandoned Russian troop transports. They watched as he passed. No one moved to stop him. One soldier uttered: “Intent on victory.”

Mr. Balakelyev, his gaze fixed and his shotgun ready, headed down the road in the direction of the booms and a tall billboard that read: “Protect the future: UKRAINE-NATO-EUROPE.”