Ukrainian President Volodymyr Zelenskiy says Ukraine's armed forces are pressing ahead with advances against Russian forces after liberating more towns in a number of areas.
Zelenskiy gave no further details in announcing in his nightly video address that the “offensive movement of our army and all our defenders continued” on October 3.
"New population centers have been liberated in several regions. Fierce fighting continues in many areas of the front," he said without specifying which settlements had been liberated.
Live Briefing: Russia's Invasion Of Ukraine
RFE/RL's Ukraine Live Briefing gives you the latest developments on Russia's invasion, Western military aid, the plight of civilians, and territorial control maps. For all of RFE/RL's coverage of the war, click here.
He added that “more and more occupiers are trying to escape, more and more losses are being borne by the enemy army, and there is a growing understanding that Russia made a mistake by going to war against Ukraine."
A day earlier Zelenskiy said its forces took full control of the strategic eastern city of Lyman in the Donbas region.
Serhiy Cherevatiy, a spokesman for the Eastern Group of the Armed Forces of Ukraine, said Ukrainian troops went on to liberate the settlement of Torske near Lyman on October 2.
There were also reports on October 3 that Ukrainian forces were recapturing towns along the west bank of the Dnipro River in southern Ukraine.
The scale of the Ukrainian advance was unconfirmed, but Vladimir Saldo, the Russian-installed leader in occupied parts of Kherson, told Russian state television that there were breakthroughs.
"There's a settlement called Dudchaniy, right along the Dnipro River, and right there, in that region, there was a breakthrough. There are settlements that are occupied by Ukrainian forces," he said.
Russian military bloggers earlier on October 3 described a Ukrainian tank advance through dozens of kilometers of territory along the riverbank.
In a rare comment by a Ukrainian official on the situation, Anton Herashchenko, an adviser to Ukraine's interior minister, posted what he said was a video of a Ukrainian soldier waving a flag in Zolota Balka, downriver from the former front line.
A senior U.S. military official said on October 3 that the attacks by Ukrainian forces have forced Russia into a “defensive crouch” in Kherson, hampering Russian efforts to resupply their frontline troops.
The official, who briefed reporters in Washington on condition of anonymity, said that so far the United States has seen only small numbers of Russian reinforcements coming into Ukraine in an effort to shore up their defenses.
The recapture of Lyman was Ukrainian forces' most significant battlefield gain in weeks and followed a counteroffensive in the Kharkiv region to the north that swept Russian forces and stunned many observers.
U.S. Defense Secretary Lloyd Austin said Washington was "very encouraged" by Ukrainian gains.
The United States will soon deliver to Ukraine four more advanced rocket systems, U.S. officials said on October 3. The High Mobility Artillery Rocket Systems, known as HIMARS, have been credited with helping the country’s military gain momentum in the war.
HIMARS have been used to strike bridges that Russia has used to supply its troops. The additional four HIMARS will be part of a new $625 million package of aid expected to be announced on October 4, according to the U.S. officials, who were quoted in U.S. media reports.
The decision marks the first time that the United States has sent more HIMARS to Ukraine since late July, and it will bring the total number delivered so far to 20.
Lyman sits at a crossroads and a switch yard for railroads, and analysts say Ukrainian troops would likely use the city as a staging post for further advances east.
The city had been the scene of intense fighting for days, with Ukrainian troops gradually encircling it and the estimated 5,000 Russian troops that were defending it.
Russia’s Defense Ministry said on October 1 that it was pulling troops out of the area "in connection with the creation of a threat of encirclement."
Unconfirmed reports said Russian forces there had suffered heavy casualties and an unknown number of soldiers were taken prisoner.
It was the latest setback for Russian President Vladimir Putin, coming one day after he proclaimed the annexation of four Ukrainian regions that have been partly occupied by Russian forces for months now.
The Donetsk region, where Lyman is located, is one of the four regions Putin claimed.
Kyiv and the West have condemned the annexation declaration as illegal and a farce.
Ramzan Kadyrov, an ally of Putin and head of Russia's Chechnya region, has said Moscow should consider using a low-yield nuclear weapon in Ukraine after the loss of Lyman.
In a statement criticizing Russian generals for the loss of Lyman, Kadyrov said it was time for the Kremlin to make use of every weapon at its disposal.
“I do not know what the Defense Ministry reports to the Supreme Commander-in-Chief, but in my personal opinion we need to take more drastic measures, including declaring martial law in the border territories and using low-yield nuclear weapons,” Kadyrov said on his Telegram channel.
Putin's declaration that Russia was annexing Donetsk, along with Luhansk, Kherson, and Zaporizhzhya, was a major escalation by the Kremlin. Observers said it signaled a further digging-in by the Russian leadership, dampening prospects for a peace deal.
SEE ALSO: Join, Flee, Or Resist: Russia Pushed To The Brink Amid Putin's Chaotic Mobilization OrderTogether with Crimea, which Moscow seized in 2014, the four regions make up around 20 percent of Ukraine, including some of its most industrialized territory.
Russia's setbacks on the battlefield also come amid reports of chaos in a mobilization ordered less than two weeks ago by Putin that has seen tens of thousands of Russian men suddenly called up into the military and tens of thousands of others fleeing abroad.
Mikhail Degtyarev, governor of the Khabarovsk region in Russia's Far East, said around half of the thousands of men called up there had been found unfit for duty and sent back home. He said he fired the region's military commissar.
"The military commissar of the Khabarovsk region, Yuri Laiko, has been suspended," Degtyaryev said in a video posted on Telegram.
This will have no impact on the fulfilment of the tasks that the president has set for us," Degtyaryev said.