BRUSSELS (Reuters) - Russia's advance in the Kharkiv area is slowing and the frontline is stabilizing after some allies lifted restrictions on Kyiv's use of donated weapons on Russian territory, U.S. Defence Secretary Lloyd Austin said on Thursday.

"What I see is a slowing of the Russians' advance and a stabilizing of that particular piece of the front. Now, I think we'll see incremental gains -- and we'll see puts and takes -- going forward," he told reporters on the sidelines of a NATO defence ministers' meeting in Brussels.

"But again, a couple of weeks ago, there was concern that we would see a significant breakthrough on the part of the Russians. I don't think we'll see that going forward."

U.S. President Joe Biden late last month approved the use of American weapons to strike targets inside Russia that were being used to attack Kharkiv, Ukraine's second largest city, which is located close to the Russian border. Moscow has condemned that decision as a form of escalation by the West.

On Tuesday, Kharkiv's mayor told Reuters that Ukraine's army in the meantime has struck missile launch positions in Russia, helping to reduce the number of attacks on the embattled city.

While missile and drone strikes continue, Ihor Terekhov said the change had helped bring relative "calm".

"That is why maybe Kharkiv has ... this period of ... calm the last couple of weeks ... that there were no great strikes as it was, for example, in May." He was speaking through a translator.

Austin said the Ukrainians were putting donated weapons to a good use.

"The Ukrainians have done a lot to fortify their defensive positions and are making good use of the weapons and munitions that they're being provided," he told a news conference. "And more of that will continue to flow in. And so in my view, they'll get stronger as time progresses."

(Reporting by Sabine Siebold in Brussels and Phil Stewart in Washington; Editing by Benoit Van Overstraeten and Peter Graff)