MYKOLAIV, Ukraine — The quick thump, thump of outgoing Ukrainian artillery echoes through the heavily fortified city hall building here in Mykolaiv in southern Ukraine, a sign of how close Russian forces have advanced in their march west along the Black Sea coast.

Mayor Oleksandr Senkevich, dressed in army green with a pistol in his pocket, barely notices as he points out the Russian positions on a map. With him was Dmytro Falko, secretary of the City Council, wearing a light flak jacket and carrying a Kalashnikov rifle in a tennis racket case on his back.

The Russians are moving in from the north, east and south, he said, the same forces that several days earlier had captured the city of Kherson, which is about 40 miles east of Mykolaiv.

By midafternoon, he said, some Russian forces had pushed into outlying areas of the city — killing a local school director and others — although Ukrainian soldiers were keeping them at bay, for now.

After a battle Friday evening, Ukrainian forces retook the Mykolaiv airport, which had earlier been captured by Russian troops, and raised the Ukrainian flag there, according to the Ukrainian military, which posted a video of the flag and jubilant troops on Twitter.

“The enemy surrounds us,” Senkevich said. “Today, they are gathering troops, and I think they want to attack us in the nearest time.”

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More about Russia’s war on Ukraine

Russian forces in the north of Ukraine have been bogged down and are largely immobile near the capital, Kyiv, and the country’s second-largest city, Kharkiv. But the troops in Ukraine’s south have been on the move.

When Russian President Vladimir Putin gave the order last week to invade, Russian forces poured out of the Crimean Peninsula, which the Kremlin annexed in 2014 and turned into a massive army garrison. From there, they spread east, where they overcame the town of Melitopol and have converged on Mariupol, which despite a nearly weeklong siege has remained in control of Ukrainian forces.

To the west, Russian troops pushed into the port city of Kherson, where the Russian commander informed Mayor Ihor Kolykhaev that he planned to establish a military administration.

As of Friday, Kolykhaev said, it appeared that Ukrainian forces positioned outside the city were blocking trucks with humanitarian assistance despite an agreement Thursday to open a humanitarian corridor, something he attributed to a miscommunication between troops on the ground and their commanders.

In the meantime, he said, the Russian troops now occupying the city — “the kind liberators,” he said sarcastically — were using the delay for their own propaganda messaging, publicly promising to provide their own assistance.

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“First, they create a critical situation, then heroically they save us so as to show on camera how everyone thanks the ‘benefactors,’” Kolykhaev said in a text message. “I give you my word, I’m doing what I can, but I do not know how long I’ll be able to hang on.”

Although the ultimate aim of Russian troops in the southern theater is unknown, the likely goal is to take Odessa, a grand city of 1 million people on the Black Sea. There, residents and officials have been preparing day and night for an attack, building tank barricades of sandbags and old steel tramlines while scanning the horizon for Russian warships approaching by sea.

But to reach Odessa by the easiest route, Russian forces will have to push through Mykolaiv and across the single drawbridge that spans the River Buh. For security, the city has ordered the bridge to remain in the up position for most of the day, allowing only about one hour for residents to evacuate. On Friday, a line of cars stretched deep into town, some of which had signs reading “children” taped to their windshields.

At the entrance to the bridge, Ukrainian troops kitted out in body armor and carrying automatic weapons stood guard. In green army boxes next to hastily erected cinder block and sandbag bunkers were shoulder-fired anti-tank missiles, provided by Britain.

If those fail to stop the Russian advance, Senkevich said, the troops were under orders to blow the bridge up.

“So far, it’s not as frightening as in Kharkiv or other cities,” said a woman named Nadezha as she prepared to cross the bridge on foot. “Our guys are protecting us well, and all our hope is in them,” she said, adding that her son was also a soldier.

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In the first days of the fighting, a lightning advance by Russian troops pushed into Mykolaiv but was repulsed by Ukrainian forces in a vicious firefight. Now, the streets are largely empty except for Ukrainian troops and the occasional lone pensioner walking with shopping bags. Most of the city’s roughly 500,000 residents appear to have fled.

Across the River Buh is a neighborhood of well-appointed homes whose residents are preparing to defend their property. One of them, who invited a reporter in for tea on condition that only his first name, Vadim, be published, showed off gruesome videos that friends had sent him from the fighting around the city. He said Russian soldiers in the region appeared to be surrendering in groups when they come under fire. The New York Times could not independently verify his claim, but observers elsewhere in the country have reported similar scenes.

“The people are still not fully angry,” said Vadim, who had a shotgun sitting on his table and said he was ready to defend his property if necessary. “But if they’re pushed over the edge, no one will be taking prisoners anymore; we’ll just shoot them.”

Senkevich, the mayor, said he and his staff were also prepared to fight it out, if and when the Russian forces came through. In addition to the pistol in his pocket, there were several automatic rifles lying around his office.

The only other things needed for the city defenders, Senkevich said, were flak jackets and helmets.

“This is the only plan, to fight to the end,” he said. “The captain leaves the ship last.”