The foreign minister's comments came as Kyiv announced two people had been killed in the "most powerful" aerial attack on the capital in weeks, and Russia reported a drone strike on military aircraft in its northwest.
Kyiv launched a counteroffensive in June after stockpiling Western-supplied weapons and building up assault battalions.
Progress has been costly and staggered but Ukrainian forces announced they had pushed through key Russian defensive lines with the capture of Robotyne in the Zaporizhzhia region this week.
"Having entrenched on the flanks of Robotyne, we are opening the way to Tokmak and, eventually, Melitopol and the administrative border with Crimea," Ukrainian Foreign Minister Dmytro Kuleba said during an earlier visit to Paris.
The Kremlin has downplayed the offensive and Yevgeny Balitsky, its official in charge of the Zaporizhzhia region, which Russia claims as its own, warned that territory beyond Robotyne would be a "mass grave for Ukraine's armed forces".
In Kyiv, an AFP reporter heard at least three explosions at around 5:00 am (0200 GMT) as part of the countrywide barrage of 28 cruise missiles and 16 attack drones.
"We heard explosions, and we could see the flashes through the window," Oksana Soloviuk, who lives next to one building hit by debris, told AFP.
Yevgen Ananenko and his father ran downstairs when they heard the blasts and metal fragments cut into the side of their building.
"If it had fallen straight into the house, I doubt we would have survived," he said.
Military officials described the attack as "the most powerful" to hit the city since the spring, and authorities said two employees of an infrastructure facility were killed by falling debris in the Shevchenkivsky district.
Prigozhin plane crash probe
The White House said meanwhile that Russia was in secret, active talks with North Korea to acquire a range of munitions and supplies for its offensive.
White House National Security spokesman John Kirby said the countries' leaders Vladimir Putin and Kim Jong Un exchanged letters pledging to increase bilateral cooperation following a visit to Pyongyang by Russian Defence Minister Sergei Shoigu.
The United States, Britain, South Korea and Japan said at the United Nations that such an arms deal would violate Security Council resolutions Russia itself has endorsed.
Kirby added that despite its denials, North Korea supplied infantry rockets and missiles to Russia last year for use by the private paramilitary group Wagner.
Its leader Yevgeny Prigozhin was killed in a plane crash in Russia last week, two months after leading a short-lived mutiny against the country's military leadership that rocked Putin's authority.
Kremlin spokesman Dmitry Peskov on Wednesday told reporters that investigators had not ruled out any cause for the crash, including foul play.
Ukraine has been stepping up drone attacks inside Russia.
It launched a wave of strikes overnight, targeting an airport near the Estonian border and the Crimean peninsula on the Black Sea, Russian authorities said.
The attack on Pskov airport, roughly 700 kilometres (more than 400 miles) from the border with Ukraine, marks the latest strike far from Ukraine's borders since Kyiv vowed to "return" the conflict to Russia in July.
State news agency TASS, citing emergency services, said four Ilyushin Il-76 heavy transport planes were damaged in the attack in Pskov, while the emergencies ministry said at least two aircraft had caught fire.
The Pskov region was previously targeted by drones in May.
Authorities in the Bryansk region near the Ukraine border, the southern Oryol region and the Kaluga and Ryazan regions, southwest and southeast of Moscow, all reported that drones had been destroyed or downed.
Air defences also destroyed a drone "heading for Moscow," the city's mayor wrote on social media, adding there were no casualties or damage caused. TASS reported that Moscow's Domodedovo and Vnukovo airports had been temporarily closed.
Moscow and other Russian regions have been targeted by almost daily drone strikes since Kyiv vowed this summer to "return" the conflict to Russia.
Black Sea tensions
Tensions have also been building on the Black Sea since Moscow exited a deal allowing maritime grain exports from Ukraine, and threatened to attack cargo ships using Ukrainian ports.
Russia's defence ministry said Wednesday that its fighter jets had destroyed several high-speed military boats in the Black Sea around midnight Moscow time.
Early Wednesday, Russian defences also repelled a "seaborne drone attack" near Sevastopol in Crimea, TASS cited the Moscow-installed governor Mikhail Razvozhayev as saying.
Sevastopol is the base of Russia's Black Sea fleet.