- Ukraine has not commented on these claims yet.
- Robotyne was one of only a handful of settlements Kyiv retook in its summer counter-offensive last year.
Ukraine has pulled back its troops from several villages in the border region of Kharkiv following continued pressure from Russian forces.
Soldiers had come under heavy fire and moved to "more advantageous positions" in two areas of the northeastern region, a military spokesman said.
Throughout the course of the two-year war, Ukraine has typically used this type of language to signify a retreat.
President Volodymyr Zelensky has cancelled all upcoming foreign trips as troops struggle to contain the new cross-border incursion, with several towns and villages coming under heavy fire.
His press secretary, Sergiy Nykyforov, said the president had "instructed that all international events scheduled for the coming days be postponed and new dates coordinated".
Moscow has claimed its forces have now taken control of two more settlements in the region - Lukyantski and Hlyboke - and the village of Robotyne, in the southern Zaporizhzhia region.
Ukraine has not commented on these claims yet.
Robotyne was one of only a handful of settlements Kyiv retook in its summer counter-offensive last year.
A spokesman for the Ukrainian military said in a statement that the decision to move troops from the Lukyantsi and Vovchansk areas was taken to "preserve the lives of our servicemen and avoid losses".
The capture of Vovchansk, though not of specific militarily significance, would represent a blow to Ukrainian morale.
The military spokesman said that the situation "remains difficult" but insisted that its forces were "not allowing the Russian occupiers to gain a foothold".
Ukraine's head of intelligence, Kyrylo Budanov, had earlier said troops had stabilised the front line.
Thousands of civilians have fled west in recent days towards Ukraine's second-largest city of Kharkiv - including from the town of Vovchansk, located 74km (45 miles) away.
Oleksiy Kharkivskiy, Vovchansk's police chief, said on social media that fighting was intense and Russian forces were establishing positions inside the town.
"The situation is extremely difficult. The enemy is taking positions on the streets of the town of Vovchansk," he said.
Kyiv has sent reinforcements to the wider Kharkiv region following Friday's incursion - seen as one of Russia's most significant ground attacks since it launched its full-scale invasion of the country in February 2022.
"Additional forces are being deployed, and there are reserves," President Zelensky's office said on Wednesday.
US Secretary of State Antony Blinken announced an additional $2bn in military aid to the Ukrainian war effort while on a visit to Kyiv.
Mr Blinken told reporters on Wednesday the fund would provide weapons "today" and invest in Ukraine's industrial base.
"We're rushing ammunition, armoured vehicles, missiles, air defences to get them to the front lines," Mr Blinken said.
"We've been through challenging times together, I have every confidence that together we will get through these difficult moments."
It comes weeks after US Congress passed a $61bn aid package last month.
Away from Kharkiv, Russia said earlier it had temporarily closed two major airports in the south-western region of Kazan after targeted Ukrainian drone attacks. Ukraine has not commented on the strike.
Russia's Foreign Ministry spokeswoman Maria Zakharova also said on Wednesday that Ukrainian attacks in Russia's Belgorod border region were a demonstration of the "criminality" of Kyiv and the Western powers which back it.
Unlike with Ukrainian territory which Russia occupies, Kyiv has reluctantly agreed with western allies to not use the missiles it provides on targets inside Russia itself.