Ukraine said on Sunday that Russian troops were advancing in four areas in the east of the country amid "fierce fighting", but reported its forces moving forward in the south.
Deputy Defence Minister Ganna Maliar said that Russian troops were advancing near Avdiivka, Mariinka, Lyman and Svatove.
"Fierce fighting is going on everywhere," Maliar wrote on social media, adding: "The situation is quite complicated".
Ukrainian forces have made gradual progress in their counteroffensive launched last month and have urged Western allies to escalate pledges of military support.
The latest developments on the battlefield came after Ukrainian officials said Russia launched its first overnight drone attack on the capital Kyiv in 12 days.
Ukraine said all the drones were downed.
Maliar also said Ukrainian troops were advancing with "partial success" on the southern flank of Bakhmut in the east and near Berdyansk and Melitopol in the south.
In the south, she said Ukrainian forces faced "intense enemy resistance, remote mining, deploying of reserves" and were only advancing "gradually".
"They are persistently and unceasingly creating conditions for as fast an advance as possible," she said.
Ukraine's military commander-in-chief Valery Zaluzhny expressed frustration in an interview published Friday at the slow deliveries of weaponry promised by the West.
It "pisses me off" that some in the West complain about the slow start and progress to the long-awaited push against Russian occupying forces, he told the Washington Post.
Zaluzhny said his Western supporters would not themselves launch an offensive without air superiority, but Ukraine is still awaiting F-16 fighter jets promised by its allies.
"I do not need 120 planes. I'm not going to threaten the whole world. A very limited number would be enough," he told the newspaper.
He also complained he has a fraction of the artillery shells that Russia is firing.
Ukrainian President Volodymyr Zelensky also spoke about F-16 training on Saturday during a visit to Kyiv by Spanish Prime Minister Pedro Sanchez.
"I believe that some partners are dragging their feet," Zelensky said, referring to F-16 training for Ukrainian pilots.
A coalition of Kyiv's European backers led by the Netherlands and Denmark has said it will help teach Ukrainian pilots, after the United States gave its green light in May.
Dutch Defence Minister Kajsa Ollongren last month said the training could start this summer.
- 'Detected and destroyed' -
Ukraine has meanwhile become increasingly adept at taking down Russian cruise missiles and drones after appealing to Western allies for greater air defence capabilities.
On Sunday, Ukrainian officials said they had successfully neutralised a new drone attack on Kyiv.
"All enemy targets in the airspace around Kyiv were detected and destroyed," said Sergiy Popko, head of the Kyiv city military administration.
In a separate statement, Ukraine's air force said Sunday that it had shot down three cruise missiles and eight Iranian-made attack drones deployed by Moscow's forces overnight.
"Eight Shaheds were launched from the southeast, and three Kalibr missiles were launched from the Black Sea," the air force said.
It did not provide any details on the Kyiv attacks.
A source familiar with the situation told AFP that no missile was shot down over Kyiv overnight.
Ruslan Kravchenko, head of the Kyiv regional military administration, said that three houses were damaged by falling debris in the Kyiv region.
One man sustained a leg injury, Kravchenko added.
Kyiv, which had been relatively spared from attacks since the beginning of the year, faced frequent nightly aerial raids in May.
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