The mayor of the Ukrainian city of Kharkiv has said that the situation there has been "calmer" since Russian missile launchers shelling it were hit by Ukrainian fire.
Ihor Terekhov's comments came nearly two weeks after the US and other Western nations gave the go-ahead for Ukraine to hit targets inside Russia near Kharkiv.
He was speaking at a conference in Germany attended by President Volodymyr Zelensky which is aimed at encouraging European nations to support and invest in Ukraine.
Russia says it has captured two Ukrainian villages as it continues its offensive begun in May.
The defence ministry said Tymkivka in Kharkiv region and Miasozharivka in Luhansk region had been taken by its forces. Ukraine has not commented.
However, on Monday Mr Zelensky said Ukraine was continuing "counter-strike activities" in Kharkiv region.
He also denied reports by the pro-Russian Chechen leader Ramzan Kadyrov that his forces had captured a village in Sumy region, which borders Russia to the west of Kharkiv, saying there was no Russian presence in the area.
On Tuesday the Ukrainian president gave his first ever speech to the Bundestag, the German parliament, making emotional references to Germany’s Cold War history of division and calling on future reparations from Russia for the damage it had caused.
“We will finish this war, in the interests of all of us, of all Europe. We will finish this war according to our conditions,” he said.
"You can understand why we are fighting so hard against Russia's attempts to divide us, to divide Ukraine. Why we are doing absolutely everything to prevent a wall between parts of our country," he said, in reference to the Berlin Wall.
He also warned of the danger to the European Union of pro-Russian rhetoric, days after far right parties, some of which are pro-Russian, made gains in EU elections.
Mr Zelensky received a standing ovation, but his speech was boycotted by the far-right AfD and the far-left BSW parties - both of which made big gains in Sunday's European elections. The BSW has campaigned against weapons deliveries to Ukraine.
The AfD characterised the boycott as a protest against Mr Zelensky as a "war president".
Ukrainian officials have reported five deaths in Russian bombardments in the last 24 hours, four of them in Kharkiv region.
Mr Terekhov said that the shelling of Kharkiv had become more frequent in the last two days, but it had generally been calmer.
"There has been a break in the shelling, which I think is connected with the fact that the equipment that Kharkiv was being shelled with has been successfully hit," he told Reuters news agency.
"As compared to May, we experienced a more or less calm week until Sunday... Therefore, it's been a bit calmer, but I can't say that it's been completely so."
Speaking alongside the Ukrainian president on Tuesday, German Chancellor Olaf Scholz said Germany was sending more air defences, including a third Patriot system, and missiles to help Ukraine.
At the end of May, US officials said President Joe Biden had allowed Ukraine to use American-supplied weapons to strike targets in Russia, but only near the Kharkiv region.
The city of Kharkiv is close to the Russian border and therefore vulnerable to attack from within Russia.
Previously Western nations had restricted targeting of weapons they provided to Russian-held areas of Ukraine, because of fears that attacking Russia itself could lead to escalation of the conflict.
