According to Hanna Malyar, the deputy defense minister of Ukraine, some of their forces are "shifting to offensive actions.".
The BBC was informed by Ukrainian military sources that a number of small-scale armoured offensive operations were underway.
Whether this marked the beginning of Ukraine's eagerly anticipated full-scale counteroffensive was not specified.
Russian defense officials had earlier claimed to have stopped a significant Ukrainian assault in Donetsk.
The "epicentre of hostilities," according to Ms. Malyar, is the eastern city of Bakhmut, where she asserted Russian forces are defending both locations.
Gen. Oleksandr Syrskyi, the commander of the Ukrainian ground forces, declared that the country's soldiers were "moving forward" toward Bakhmut and had destroyed a Russian position close by.
Long anticipated is a significant Ukrainian counteroffensive, but Kyiv has already declared it won't announce its launch in advance.
The amount of military activity has significantly increased, though Ukraine claims to have made small gains elsewhere on the front line.
The most recent reports are thus being interpreted as a brand-new indication that the anticipated Ukrainian push may have started.
Using six mechanized and two tank battalions, the Russian defense ministry claimed that Ukraine had also begun a "large-scale offensive" in the Donetsk region on Sunday.
In what Kyiv considered to be the most exposed area of the front line, the Ukrainians allegedly attempted to breach Russian defenses, but they "did not achieve their tasks, it had no success," according to the report.
Military vehicles were seen being heavily fired upon in fields in footage of what Russia claimed to be the Donetsk battle. Russian officials assert that 16 tanks and 300 soldiers were killed.
The claims made by Moscow, however, have not been independently confirmed.
And on Monday, the Ukrainian military asserted that it was unaware of any significant attacks taking place nearby.
A spokesperson for the Ukrainian army told Reuters, "We do not have such information and we do not comment on any type of fake.".
If the video of the armored vehicles coming under intense fire is real, it illustrates the fierce opposition Ukrainian forces will encounter as they attempt to liberate more land.
Even if it is not what it seems, Moscow is still attempting to take control of the story.
The amount of information coming out of Ukraine about when and how its counteroffensive might develop has significantly increased.
Ukraine has been preparing for this action for several weeks. However, it has sought as much time as possible to prepare its soldiers and acquire military hardware from Western allies.
Officials in Kiev have issued a warning against public speculation about the offensive, claiming that it could aid the adversary.
Plans adore quiet. There won't be a start announcement, the defense ministry declared in a video shared on Telegram on Sunday. Armed and masked soldiers were seen holding their fingers to their lips in the video.
The liberation of territory that Russia annexed as recently as nine years ago will take some time for Ukraine to accomplish.
Moscow has had time to get ready. It implies that even if Ukraine is able to launch a counteroffensive, it will take time.
Much is at risk because the Ukrainian government must demonstrate to its citizens and Western allies that it is capable of breaching Russian defenses, ending the military standoff, and reclaiming some of its sovereign territory.
In another location, near the Ukrainian border in Belgorod, fighters opposed to the Moscow government claim to have captured some Russian soldiers.
The Liberty of Russia Legion (FRL), which made the assertion, claimed that the announcement was a joint one with the Russian Volunteer Corps (RDK).
Vladimir Putin's government is being challenged by both groups. They reject his February 2017 launch of a full-scale invasion of Ukraine.
Vyacheslav Gladkov, the top official in Belgorod, responded by stating that he had consented to meet the soldiers' captors if they were still alive. Later on though, the fighters claimed that the governor "had not found the courage" to meet them and that they would be turning over their prisoners to Ukraine.
Despite Kiev's denials, Russia has accused Ukraine of being directly responsible for recent attacks in its border regions.
Following a drone attack on Monday morning, Belgorod authorities reported that an energy plant was on fire. .
Governor Vladislav Shapsha reported that two drones fell onto a major road in Russia's Kaluga region, which borders the southern neighborhoods surrounding Moscow. Since there had not been an explosion, the area had been cordoned off, according to Mr. Shapsha.
Although neither attack has been independently confirmed, Moscow claims that Ukraine has routinely used drones to attack the Belgorod region.
Volodymyr Zelesnky, the president of Ukraine, met with James Cleverly, the foreign secretary of the UK, on Monday in Kiev.
