ZAPORIZKA REGION, Ukraine — The day after the war began, after their unit was nearly wiped out in a missile strike, Ukrainian Sgt. Oleksandr Gorvat presented his girlfriend and commanding officer, First Lt. Olena Petyak, a ring he had twisted together from wire and asked for her hand in marriage.
“Officially we’re not supposed to serve together, but we are not officially married,” he explained on Friday, amid the whoosh of Grad rockets being fired at nearby Russian positions. “That is for after the war. As soon as we win.”
Together with their unit, the 128th Separate Mountain Assault Brigade, the couple, both 25, were dug into a frontline position in the Zaporizka region of south-central Ukraine, east of the Dnipro River and only about two miles from where Russian forces were attempting to overrun more territory.
Fierce fighting was underway on Friday across a band of southeastern Ukraine, in and around major towns like Polohy, Orikhiv and Vasylivka, which is on the banks of the Dnipro. It fell to the troops of the 128th to prevent Russian forces from pushing farther north toward the important industrial city of Zaporizhzhia, just 20 miles north of Vasylivka on the river.
The Kremlin has achieved one of its strategic goals, seizing a strip of land along the Azov Sea, linking the Donbas region in the east, now the focus of the war, with Crimea, the peninsula President Vladimir V. Putin invaded and annexed in 2014. The only significant pocket of resistance remaining is a sprawling steel mill complex in the ruined port city of Mariupol, where Ukrainian fighters and civilians are in underground bunkers, under heavy bombardment.
But the Russians were attempting this week to expand that ribbon of territory, pushing north from the coast toward Zaporizhzhia. Other Russian forces were pushing west through Donbas, where on Friday some of the heaviest combat was being waged around the city of Sievierodonetsk and the town of Popasna. Moscow’s army was also advancing southward from the city of Izium. Altogether, the front line is about 300 miles long.
Moscow’s separatist proxies in Donbas, backed by Russian equipment and troops, have held part of the region since 2014, and Russia has said that it aims to expand its territory there. How far Mr. Putin will go is unclear, but the Kremlin appears intent on trapping much of the Ukrainian military in a pincer and destroying it.
Lieutenant Petyak, who is second in command of the brigade, said the goal in the Zaporizhzhia region — the southwestern part of that front line — was not just to hold the Russians at a standstill but to push them back.
“The enemy is constantly firing with artillery, tanks, Grads, and aviation in our direction,” she said. “They want to knock out this section, but they won’t be able to do it because we’re here. On the contrary they are going to have to give up their positions because I’m certain that sometime soon we will push forward and take the remainder of the land that they’ve been able to temporarily occupy.”
That may prove a challenge, even for the Ukrainian forces, which have surprised military analysts and professional soldiers with their fierce and effective defense since the start of the war.
After Mr. Putin ordered the invasion of Ukraine, Russian forces based in the Crimean Peninsula, some of the country’s most skilled and well-equipped, lunged north, gobbling up territory in southern Ukraine both in the direction of Kherson, west of the Dnipro, and east toward Mariupol.
Early in the morning of Feb. 24, the soldiers of the 128th brigade learned the war had begun when a Russian cruise missile hit their base, just missing the barracks where they slept. The troops were able to escape into the nearby woods.
It was the next day, as they scrambled to regroup and join the combat against the invading Russians that Sergeant Gorvat proposed.
At first the brigade was deployed in the vicinity of Melitopol, a southern city about midway between Crimea and Zaporizhzhia. But they have been pushed back nearly 70 miles to the north. They are now entrenched in a patch of woods wedged between wheat fields that are bright green with spring growth.
Ukrainians who live in the coastal territory that Russia has seized continue to surge north seeking refuge in Ukrainian-held lands. Convoys of cars and buses, laden with suitcases, arrive regularly at the parking lot of a home goods store in Zaporizhzhia. Many arrive with unsettling tales of the Russian occupation.
“It’s total lawlessness,” said Natalya Gorbova, who arrived in Zaporizhzhia on Thursday with her 17-year old son, Egor. They had fled Melitopol, whose mayor was kidnapped by Russian forces and dragged from his office with a bag over his head. He was only released after Ukraine agreed to a prisoner swap.
“If you stay home, it’s fine,” Ms. Gorbova said, “but there are these guys walking around with guns who do whatever they want.”
In Ukrainian territory, she said, “it’s easier to breathe.”
Ukraine’s front line positions buzz with surveillance drones that Russian forces use to target their artillery. At one point on Friday, Capt. Vitaliy Nevinsky, the commander of the 128th, dispersed a group of soldiers chatting close together around a campfire, lest a drone direct an artillery strike into the middle of their gathering.
The first weeks of the war were a baptism by fire for the 128th. At one point, Captain Nevinsky explained, his forces were surrounded and had to punch their way through the Russian lines. Captain Nevinsky, 25, said he was riding on a tank, covering the unit’s escape when it was hit by a shell. He suffered shrapnel wounds and a concussion, but returned to the front lines two weeks later.
His brigade is better equipped now, he said, with antitank missiles provided by the Americans and the British, as well as Stinger antiaircraft missiles and other advanced weapons systems. These have helped slow the Russian forces down, he said. This week, he said, the brigade has taken out two Russian T-72 tanks that strayed too close to their positions.
“We are on our own land,” he said. “We are defending ourselves and knocking out this horde, this invasion of our territory.”