Stating the incursion’s aims for the first time, President Volodymyr Zelenskyy says Ukraine needs border ‘buffer zone’.
Ukraine says it has destroyed a second bridge across the River Seym which winds through Russia’s Kursk region.
It is the second attack on a bridge in the region in a matter of days and comes as Ukraine presses a cross-border offensive that began on August 6.
On Friday, it said it had struck a bridge in the Russian town of Glushkovo.
“Minus one more bridge,” Ukrainian Air Force Commander Mykola Oleshchuk wrote on Telegram on Sunday, publishing an aerial video of a blast tearing through the bridge near the Russian town of Zvannoye.
He said the attacks were designed to disrupt Russian supply lines.
“The Air Force aviation continues to deprive the enemy of logistical capabilities with precision air strikes,” Oleshchuk said, without giving a date for the attack.
Hours after the attack, Ukrainian President Volodymyr Zelenskyy praised the military’s incursion and stated its aims for the first time.
“Our guys are doing a great job in all areas,” he said in his evening address on Sunday.
“It is now our primary task in defensive operations overall: to destroy as much Russian war potential as possible and conduct maximum counteroffensive actions. This includes creating a buffer zone on the aggressor’s territory -– our operation in the Kursk region.”
Pro-Kremlin military bloggers acknowledged the destruction of the first bridge near Glushkovo, which is about 12km (7.5 miles) north of the Ukrainian border, saying it would disrupt supply lines.
Zvannoe is located a further 8km (5 miles) to the northwest.
According to Russia’s Mash news site, the attacks left only one bridge in the area intact, potentially complicating further Moscow’s attempts to replenish its forces and evacuate civilians.
Until now, Kyiv has said little about the goals of the surprise incursion, which began with tanks and other armoured vehicles, the largest attack on Russia since World War II.
Ukraine’s military chief, Oleksandr Syrskii, claimed last week that his forces had advanced across 1,000sq km (390sq miles) of Kursk, although it was not possible to independently verify the extent of its control.
The incursion has helped boost Ukrainian morale as Russia pushes forward in Ukraine’s eastern Donetsk region.
On Sunday, Moscow claimed to have taken the village of Svyrydonivka, about 15km (nine miles) from Pokrovsk, which is a key logistics hub for Ukrainian troops and towns across the eastern front.
Zelenskyy has urged Kyiv’s allies to lift the remaining restrictions on the use of Western weapons on targets deeper inside Russia, including in Kursk, saying his troops could deprive Moscow “of any ability to advance and cause destruction” if granted sufficient long-range capabilities.
Ukraine says bases inside Russia have been used to launch long-range attacks on Ukraine’s cities and energy infrastructure, causing significant damage and casualties.
On Sunday, Moscow targeted the capital Kyiv with ballistic missiles for a third time this month, according to the head of the municipal military administration, Serhiy Popko.
Zelenskyy said Russia had launched more than 40 missiles, 750 guided aerial bombs and 200 attack drones against Ukrainian villages and cities in the past week alone.