Ukraine's military says Russia is massing troops on the right bank of the Dnieper River as both sides appear poised for what could be a key battle for the city of Kherson in Ukraine's south.

The General Staff of the Ukrainian Armed Forces said on October 28 that Moscow has sent in up to 1,000 recently mobilized soldiers to make up for personnel losses suffered at the hands of an ongoing Ukrainian counteroffensive in Kherson region.

"The command of the Russian occupying forces, in order to avoid panic among the personnel, is trying by all means to hide the real losses of servicemen.... There is a strengthening of the enemy group on the right bank of the temporarily occupied territory of the Kherson region with mobilized servicemen numbering up to 1,000 people," the General Staff said in a statement.

It said that civilians continued to be moved from Kherson city on the right bank of the Dnieper onto the left bank.

Ukraine has pushed ahead with an offensive to reclaim the Kherson region and its capital of the same name, which Russian forces captured during the first days of the war.

Ukrainian forces were surrounding Kherson from the west and attacking Russia’s foothold on the right bank of the Dnieper River.

However, tough terrain and bad weather held up the Ukrainian Army's main advance in Kherson, officials said.

Kherson, one of four partially occupied provinces that Russia proclaimed to have seized last month, controls the only land route to the Crimean Peninsula that Russia illegally annexed in 2014 and the mouth of the Dnieper that bisects Ukraine.

Russia-appointed officials in Kherson said on October 27 that more than 70,000 people have left the city, including members of the Moscow-installed regional administration.

The Ukrainian military said on October 28 that forces had killed 44 Russian soldiers in the past 24 hours, adding that its forces had destroyed an ammunition depot and a hangar with equipment.

The claim could not be independently verified.

However, Chechen leader Ramzan Kadyrov, a close ally of Russian President Vladimir Putin, said 23 of his soldiers were killed and another 58 wounded in a Ukrainian artillery attack this week in Kherson. The comments were unusual as pro-Moscow forces have rarely admitted to major battlefield losses.

WATCH: A local official told Russian conscripts "You are not cannon fodder" in a video published online recently. The men responded by angrily shouting that, actually, that's exactly what they are. The incident, in the Ardatovsky district some 360 kilometers east of Moscow, followed a stream of videos in which Russian conscripts complain of old equipment and poor training.

In the eastern region of Donetsk, Russian shelling killed four local residents, Pavlo Kyrylenko, the head of the region's military administration, said on October 28.

Russian air strikes, drone attacks, and shelling of Ukraine's energy infrastructure were forcing electricity cuts in the capital, Kyiv, and other places, officials said.

A drone attack on October 27 hit an energy facility in the capital, causing a fire, said Oleksiy Kuleba, governor of the Kyiv region. The latest attacks inflicted “very serious damage,” he said.

But Ukrainian President Volodymyr Zelenskiy said Ukrainians will not be cowed by such tactics.

"Shelling will not break us -- to hear the enemy's anthem on our land is scarier than the enemy's rockets in our sky," Zelenskiy said in his regular video address on October 27 as he stood outside in the dark next to the wreckage of a downed drone.

WATCH: Ukrainian troops are targeting Russian-launched drones, fighter planes, and helicopters, using Soviet-era antiaircraft systems with limited radar capabilities. They also use Western-supplied, shoulder-launched missiles like the Stinger, but factors such as the weather can have a major impact on their effectiveness.

Meanwhile, U.S. officials quoted by Reuters and the Associated Press said the United States is preparing a new $275 million package of military assistance for Ukraine to bolster its counteroffensive against Russian forces.

The officials, who spoke on condition of anonymity, said there are no major new weapons in the U.S. package, which is expected to be announced as early as October 28.

Instead, the U.S. aid is largely aimed at restocking thousands of rounds of ammunition for weapons systems already there, including for the High Mobility Artillery Rocket Systems, known as HIMARS, which Ukraine has been successfully using in its counteroffensive against Russia.

White House national-security spokesperson John Kirby declined to confirm details of the package in a CNN interview, saying only that a new tranche of weaponry for Ukraine would be announced "very, very soon."

(KB/RFE-RL)