Ukrainian soldiers are pushing deeper into the Kursk region of southern Russia for a second week and now control more than 280 square miles of enemy territory along the border. The effort defied expectations that the sortie was meant as a brief diversion in the battle with Russia.

Kyiv says its forces have also captured more than 100 Russian prisoners that will eventually be swapped for Ukrainian POWs. In Washington, Pentagon and White House officials said Thursday they have reports that Moscow is already scrambling to move more troops as it struggles to contain the Ukrainian offensive.

Ukrainian President Volodymyr Zelenskyy claimed on Thursday that his country’s troops had taken full control of Sudzha, the largest Russian town to fall since the start of the incursion more than a week ago, The Associated Press reported.

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While small, Sudzha is the administrative center for the border area of Russia’s Kursk region. The town of 5,000 people also hosts a processing station for Russian natural gas arriving from western Siberia, which then are sent along through Ukrainian pipelines to markets in Europe, accounting for about 3% of European gas imports.

Mr. Zelenskyy said Ukraine was setting up a military command office in Sudzha, hinting at plans to remain in the Kursk region for the long term, according to the AP report. Russian defense officials defense ministry said Thursday that their forces had blocked Ukrainian attempts to take several other communities.

One of the primary military objectives in the Kursk operation is to force a pullback of Russian artillery so the guns couldn’t be used against civilian targets. Another is to cut off logistics routes that allow Russian commanders to rapidly shift reserves along the front line, Ukrainian officials said.

“Ukraine does not set itself the goal of occupying this territory, but is waging a war specifically within the framework of defense and destroying only military facilities,” Mykhailo Podolyak, a senior adviser to Mr. Zelenskyy, told the independent Russian news outlet Meduza. “Social facilities remain under the control of the Russian Federation — they are of no value to Ukraine.”

Mr. Podolyak said they also want to give Russians living near the border an idea of what Ukrainians have been forced to endure since President Vladimir Putin ordered the invasion in February 2022.

“When entering the Kursk region, we saw how shocked people were. They live in a different reality,” he said. “It seems to them that the war is already going on almost on the territory of European countries and they have no risk. Now they see a completely different situation.”

The Ukrainian drive into the Kursk Oblast, the largest land attack into Russia since World War II, also illustrates the failure of leadership in the Kremlin, Mr. Podolyak told Meduza.

“They cannot understand what is happening [and] are incapable of making quick and effective decisions,” he said. “Their actions once again prove that they are weak in managing the situation.”

Kyiv’s operation was carried out in great secrecy, without the knowledge of the U.S. government and other allies that have helped supply the Ukrainian armed forces. On Thursday, Pentagon officials again confirmed that they were not given a heads-up that Ukrainian soldiers were moving across the Russian border.

“We were not made aware of this operation, but that doesn’t mean it’s an intelligence failure,” Sabrina Singh, a Pentagon spokesperson, told reporters. “We’re working with the Ukrainians to better understand their objectives.”

The Biden administration has restricted the use of American-supplied weapons to Russian targets within Ukraine or immediately across the border. Ms. Singh said the policy hadn’t changed.

“We’re always assessing what they need on the battlefield to be successful. We believe you’re seeing those successes come to fruition,” she said. “The president has been clear — we’re going to stand with Ukraine for as long as it takes.”

Mr. Putin’s government has denounced the Ukrainian operation as a “terrorist strike,” but the inability to stem territorial losses is proving a major embarrassment for the Kremlin.

Dmitry Polyansky, deputy ambassador at Russia’s United Nations mission, dismissed the Ukrainian assault on Kursk a “mad and reckless operation” and said Russia would soon restore control. “What’s happening in Kursk is the incursion of terrorist sabotage groups,” he said. “There is an incursion because there are forests that are very difficult to control.”

• This article was based in part on wire service reports.