Russian and Ukrainian forces are reporting intense fighting along the border of Ukraine's eastern Donetsk and southern Zaporizhzhia regions as Kyiv's military attempts to break through the front lines and recapture territory in an ongoing counteroffensive.

The new reports came as Russian missiles attacked the central Ukrainian city of Kryvyi Rih early Tuesday, killing at least three people and injuring 25, according to Serhii Lysak, head of the Dnipropetrovsk region military administration.

Air defenses shot down three cruise missiles over the city but there were also "incomings," he said that hit civilian infrastructure, adding that a five-story apartment building was on fire.

The latest battle reports came from Moscow-backed officials and military bloggers who detailed clashes south of the town of Velyka Novosilka along both sides of the Mokri Yaly River, where Ukrainian forces have made gains in recent days.

Ukraine on Saturday seized several small villages along the river, according to geolocated video. And on Sunday, Ukraine's deputy defense minister Hanna Maliar said Kyiv's advances in the area amount to between 5 and 10 kilometers (3 to 6 miles).

Late Monday, a senior Russia-appointed official, Vladimir Rogov, spoke of heavy fighting in an area known as the Vremivka Ridge, claiming that higher ground remained under Russian control.

Rogov, a member of the Russian-installed Zaporizhzhia administration, said on Telegram that Russian attack helicopters were in action, and that in the vicinity of the village of Urozhaine, "reciprocal shelling and heavy fighting of ultra-high intensity continues."

Rogov conceded that Ukrainian forces were "holding their positions on the northern and eastern outskirts of the village."

Russian forces are trying to repel Ukraine's breakthrough with counterattacks, according to the unofficial Russian Telegram channel, Operatsiya Z.

The channel said Monday that Ukrainian forces were trying to take higher ground to "create conditions for advancing," and assessed that their aim was to advance toward the Russian-occupied hub of Staromlynivka.

Battle for Makarivka

In the Donetsk village of Makarivka, Ukrainian forces had "already been driven out by the quick and effective counterattack of the 127th Division," said Rogov, the Moscow-backed official. CNN cannot independently verify battlefield reports and other accounts paint a gloomier picture for Russian forces around Makarivka.

Ukrainian deputy defense minister Maliar said Monday that Makarivka was one of seven villages recaptured by Ukrainian forces in the past week.

Russian military bloggers have also been reporting intense combat in the area, with one Telegram channel called "Our Donetsk" saying the Ukrainians "managed to deepen and advance through the wooded areas, threatening with further advance to encircle" nearby Russian units.

There is no way to verify these unofficial reports, but they are consistent with a pattern in the fighting that has evolved in the last week.

"Our Donetsk" acknowledged that Russian troops had been forced to abandon Neskuchne -- just south of Velyka Novosilka -- for a second time, "retreating to positions where they would not be encircled."

It said the Ukrainians were "accumulating forces" in the area, and heavy fighting continued.

Meanwhile, one of the most prominent Russian bloggers, Voenkor Kotenok, said late Monday that a senior Russian officer was killed as troops of Russia's Fifth Army were forced to leave Makarivka.

Voenkor, who has 423,000 subscribers, said in a Telegram post that "as a result of an enemy missile attack, the Chief of Staff of the 35th Combined Arms Army, Major General Sergei Goryachev, was killed."

There is no independent verification of the death of Goryachev, a highly experienced commander, and no word from the Russian Defense Ministry.

Voenkor said that "according to representatives of the command of the United Group of Forces (S), the army has lost today one of the brightest and most effective military leaders."

Another well-known Russian military blogger, WarGonzo, acknowledged Monday that earlier "victorious statements" about the situation in Makarivka were "premature."

"The settlement is still a place of fierce fighting...The enemy is bringing in infantry in small groups, using light equipment, which makes it difficult to defeat them quickly," the blogger said on Telegram.

"Despite expectations, we have failed to retake the village by the end of the day. We hope there will be success in this regard tomorrow."

By contrast, Russian military bloggers are claiming that Ukrainian efforts to advance south of Orikhiv, in another part of the southern front, have been resisted, with several saying the Ukrainians had lost a significant number of demining tanks in an area known to have been heavily fortified by the Russians with minefields and tank traps.

Geolocated video appears to show Ukrainian armor losses in this area.

'Ultimate goal'

In his nightly address Monday, Ukrainian President Volodymyr Zelensky said the fighting in the Donetsk-Zaporizhzhia border region is tough but Ukrainian forces are recapturing territory.

"The battles are fierce, but we are moving forward, and this is very important. The enemy's losses are exactly what we need," Zelensky said.

"Although the weather is unfavorable these days -- the rains make our task more difficult -- the strength of our warriors still yields results."

Zelensky also said "the most important and hottest" operational areas are in the Tavria and the Khortytsia directions.

The commander of the Ukrainian Ground Forces and the general of the Tavria operational-strategic group reported "on the success we have achieved, on the front areas where we need to reinforce and on the actions we can take to break more Russian positions," Zelensky said.

Zelensky's chief diplomatic adviser Igor Zhovkva told CNN Monday that the "ultimate goal of the counteroffensive campaign is to win back all the territories, including Crimea."

Zhovkva would not give details on the counteroffensive actions underway.

He also sought to tamp down any expectations that the campaign would achieve rapid results, saying it could take many months for Ukraine to achieve its aims.