Ukrainian forces have stepped up artillery strikes and ground assaults in a flurry of military activity that American officials suggested on Monday could signal that Kyiv’s long-planned counteroffensive against Russia had begun.

The fighting, which began on Sunday, was raging along several points on the front line, but farther to the east of where many analysts had expected Ukraine’s counteroffensive to launch. Even if it has started in that eastern area, experts said, the battle would allow Kyiv’s troops to try to accomplish the same goal: Head south toward the Sea of Azov and cut off the land bridge connecting occupied Crimea to mainland Russia.

The Russian Ministry of Defense said on Monday that a major Ukrainian operation had begun at five locations in the eastern Donetsk region and that it had repelled the assaults and inflicted casualties on Ukrainian forces. Moscow’s account could not be independently corroborated.

Ukraine’s deputy minister of defense, Hanna Malyar, said on the Telegram messaging app that Kyiv’s forces in some areas were “moving to offensive actions” in the war that began when Russia invaded its neighbor 15 months ago. But she stopped short of saying it was a decisive new phase in the war.

“A defensive operation includes everything,” she said, “including counteroffensive actions.”

Pro-Russian bloggers noted that a strong Ukrainian attack had begun Monday morning near the town of Velyka Novosilka, in Donetsk. Mikhail Zvinchuk, a pro-Russian blogger who writes under the pseudonym Rybar, described intense fighting as Ukrainian soldiers in German-made Leopard tanks seized control of the village of Novodonetske on Monday evening, a possible sign that Kyiv had pushed its NATO-trained forces into the battle.

He said the battles were being contested “under heavy artillery fire.”

Aleksandr Khodakovsky, the commander of a Russian proxy group, also described seeing Leopard tanks during the fighting near Novodonetske, where, he said, Ukrainian forces had “felt out our weak spots.”

President Volodymyr Zelensky of Ukraine, in his overnight address, expressed gratitude to “to all our defenders who gave us the news we expect.”

“We see how hysterically Russia perceives every step we take there, every position we take,” he added. “The enemy knows that Ukraine will win. They see it. They feel it thanks to your strikes, soldiers, and in particular in the Donetsk region.”

Ukraine has long said it will make no formal announcement about the start of its counteroffensive. And Ukrainian officials have not told their American counterparts exactly when the battles will start, but provided them with a time frame for when they intended to begin the push against Russian forces. Sunday fell within that time frame, said U.S. officials, who spoke on the condition of anonymity to discuss sensitive intelligence.

The American officials based their assessment that Kyiv had most likely begun its counteroffensive partly on information from U.S. military satellites, which had detected increased movement from the Ukrainian military positions. The satellites have infrared capabilities to track artillery fire and missile launches.

U.S. military analysts also said they believed that Ukrainian units had begun an initial push to determine the positions and strength of Russia’s forces — a traditional tactic that Americans had been training Ukrainian forces to use.

An American official said that testing for potential weaknesses in Russian defenses, manpower and morale — what the U.S. military calls “reconnaissance by force” — would most likely continue for several days. If successful, the official said, the main thrust of the Ukrainian counteroffensive would become more evident during that time.

U.S. and Ukrainian officials would also be watching closely to see how Russia reacts to these attacks spread out along the front lines.

At the White House, John Kirby, a spokesman for the National Security Council, said he would not go beyond the statement that Ukrainian officials made.

“What I can speak to is how hard we worked to prepare them to be ready,” Mr. Kirby said. “The president is confident we did everything we could over the last seven, eight months or more to make sure they had the capabilities to be successful.”

Much is riding on Kyiv’s ability to reclaim territory lost to Russia since the war began. Ukrainian officials say they must move as quickly as possible to liberate people living under Russian occupation and subject to abuses, including torture and the forced deportation of children to Russia.

Success could also support Ukraine’s push for longer-term commitments from the West for additional military aid and security guarantees. It could also strengthen the hand of Mr. Zelensky in any peace talks with Russia. Failure, or a lack of demonstrably quick progress, could complicate Kyiv’s push for additional security guarantees at a NATO summit this summer.

The front line in southern and eastern Ukraine has been largely static for months, with the exception of intense fighting in the eastern city of Bakhmut and operations by small Ukrainian units. In northeastern Ukraine, anti-Kremlin forces have been staging cross-border raids into Russia since last month.

Weeks after Russian forces captured Bakhmut, the commander of Ukraine’s ground forces said on Monday that Kyiv’s troops were making an advance near the ruined city, although the extent of any gains was unclear.

Tanks from an assault brigade destroyed enemy positions, the commander, Gen. Oleksandr Syrsky, said on Telegram. The post also said that Ukrainian forces had made progress in a small wooded area during an assault on enemy positions.

Ms. Malyar, Ukraine’s deputy minister of defense, said on Telegram that Bakhmut remained “the epicenter of hostilities.”

“There, we are moving along a fairly wide front,” she continued, adding, “The enemy is on the defensive.”

One difficulty in determining the exact start of a counteroffensive is that the fighting could begin with feints or diversions. And to carry out a successful counterattack after months of planning, Ukrainian troops must navigate mostly flat, unforgiving terrain and staunch Russian defenses.

The operation is expected to involve thousands of Ukrainian troops, including many equipped with newer and more advanced Western equipment like armored personnel carriers and tanks.

Western officials have long thought that a counteroffensive would focus on southern Ukraine as part of a strategy to sever the land bridge between western Russia and Crimea. But no matter where Ukraine attacks along a front line stretching hundreds of miles, Russia’s defenses will be formidable.

Moscow’s forces have had months to dig in, lay minefields and prepare entrenchments. The Pentagon has trained new Ukrainian units with the hope that they have the power to turn the tide, but some American officials have noted that dug-in Russian defenders could prove difficult to dislodge.

Ukrainian forces have also faced challenges as Russian formations have become adept at using drones to pinpoint targets for artillery strikes. Kyiv’s troops have found it difficult, often under withering fire, to coordinate troop movements, tanks and artillery support effectively enough to achieve a breakthrough.

Igor Girkin, a pro-Russian former paramilitary commander who uses the nom de guerre Igor Strelkov on Telegram, said Russia’s forces had had time to prepare for a Ukrainian counterattack — unlike last year, he wrote, when they created “ideal conditions” for Kyiv’s forces to advance in Kharkiv.

But he said that a significant breakthrough by Ukrainian forces in the Novodonetske area would give Kyiv an opening to drive a wedge between Donetsk and Mariupol in southern Ukraine and cut off communications between the two Russian-held cities.

“If the enemy manages to break through deep enough and on a wide sector of the front (which it is trying to do),” Mr. Girkin wrote, “then its advantage in number of units and formations will be difficult to stop.”

Even as battlefield activities surged, diplomatic efforts to stop the war continued. Pope Francis sent a cardinal to Ukraine on a two-day trip to discuss prospects for peace, the Vatican said on Monday.

There was no immediate comment from the Ukrainian government, which has expressed skepticism about the pope’s role as a potential mediator.

Reporting was contributed by Adam Entous, Paul Sonne, Daniel Victor, Matthew Mpoke Bigg and Gaia Pianigiani.