Blinken, in Kyiv, Is Anticipated to Announce $1 Billion in New U.S. Assist to Ukraine

But analysts said that does not necessarily mean they have secured the territory, in an offensive that has met fierce resistance and made progress in small steps and at a high cost in casualties and equipment.

For their part, Ukrainian military officials refrained from making any sweeping claims.

Oleksandr Shtupun, a spokesman for the Ukrainian Army in the south, told national television that the Russian trenches and dugouts that Kyiv’s forces were now encountering near Verbove were “not as strong” as at the first line of defense. But he said Russian minefields would complicate Ukraine’s push forward, and military analysts have suggested that Moscow may have reinforced its defenses outside Robotyne with more troops.

Ukrainians forces enjoyed surprising successes earlier in the war by holding Kyiv, the capital, and repelling Russian forces at the end of March last year. Later, in September, they were able to drive Russian soldiers from vast swaths of land they had seized in the northeast of the country and then again in the south two months later.

But this counteroffensive, which began almost three months ago, has been another matter. With the attack long expected, Russian forces had plenty of time to dig in, building barriers and laying mines, and rendering vast parts of the landscape deadly with a single misstep.

The Ukrainian military aims to reclaim land in the south and east of the country. In the south, its goal is to reach the Sea of Azov and drive a wedge through Russian-occupied territory, and its main effort so far has been in the direction of the city of Melitopol.

The retaking of Robotyne last week marked a significant moment in Ukraine’s efforts to sever Moscow’s supply lines to occupied Crimea, but Kyiv’s forces still have a long way to go. Now, their push from Robotyne east to Verbove is aimed at widening the breach in Russia’s layers of defenses, two military analysts, Michael Kofman and Rob Lee, wrote in a paper published on Monday.

Expanding that breach, they said, is critical because “a narrow advance could leave its forces vulnerable to counterattacks on the flanks.” A wider gap would also allow Ukrainian forces to bring in more equipment and personnel to support their advance south.

A strategic target in this push appears to be the city of Tokmak, a road-and-rail hub about 15 miles south of Robotyne. To reach that city, Ukrainian forces would have to fully break through the defenses around Verbove and then breach additional layers.

That suggests a slow and exhausting fight that could take several more months, with the likelihood of heavy casualties on both sides.

On Tuesday, Ukraine’s president, Volodymyr Zelensky, said he had once again visited the front lines — the latest in a series of trips that appear aimed at bolstering the morale of troops waging a bloody and slow battle.

Mr. Zelensky said he had visited combat brigades fighting near the ruined eastern city of Bakhmut, which Russian forces seized in the spring after a nearly yearlong battle. Ukrainian fighters have since managed to regain some land around it.

His office said the Ukrainian leader had discussed “the problematic issues and needs of the units,” among them the provision of artillery shells and air-defense missiles.

Late on Monday, in his nightly video address, Mr. Zelensky said, “It is extremely important to support our warriors, to communicate with the brigade and battalion commanders,” and reported that he had visited 11 brigades in the Donetsk and Zaporizhzhia regions that day.

The subject of ammunition also came up during his visits with troops in Donetsk on Monday, according to Mr. Zelensky’s office. It said that commanders had mentioned the growing need for drones and “anti-drone weapons, insufficient manning of units and a shortage of certain types of ammunition.”