Zelenskiy Says Intense Fighting Showing 'Positive Results,' As West Responds To Putin's Nuclear Threat.

A Ukrainian soldier reacts as he receives an injection during an evacuation of injured soldiers in a region near the retaken village of Shchurove on September 25.

Ukraine's president said late on September 25 that there was fierce fighting taking place on the front lines of its 7-month-old defense against Russia's invasion but that Kyiv was seeing "positive results."

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President Volodymyr Zelenskiy's battlefield assessment came after he warned in a broadcast interview earlier in the day against dismissing Russian President Vladimir Putin's nuclear threats as Moscow's forces lose ground.

Meanwhile, new British Prime Prime Minister Liz Truss downplayed Putin's recent statements as "saber-rattling" and "bogus threats," and U.S. national-security adviser Jake Sullivan said Washington had outlined to Moscow the "catastrophic consequences" it would face if it used nuclear weapons against Ukraine.

In his nightly video address, Zelenskiy claimed gains against Russian forces in the eastern Donetsk, northeastern Kharkiv, and the southern Mykolayiv and Zaporizhzhya regions.

"We have positive results in several directions." he said.

Russia and its separatist allies in the Donetsk, Luhansk, Kherson, and Zaporizhzhya regions of Ukraine have been holding votes on possible independence and union with Russia that they call referendums but Kyiv and many in the international community have said are a sham.

The votes are scheduled to conclude on September 27.

They were announced amid Ukrainian counteroffensives in northeastern and eastern Ukraine that Kyiv has said have wrested back thousands of square kilometers this month.

Putin and other Russian officials have suggested the votes will result in an irreversible transformation of those areas to make them part of Russia. And Putin suggested this week that Moscow could use all means at its disposal to defend them.

After his speech to the UN General Assembly in New York, Russian Foreign Minister Sergei Lavrov was asked if Moscow would have grounds for using nuclear weapons to defend the annexed regions.

He said territory "further enshrined" in Russia's constitution "is under the full protection of the state."

Zelenskiy, who has vowed Ukraine will reclaim all of its lost territory, said in an interview with a U.S. broadcaster on September 25 that "maybe yesterday it was a bluff. Now, it could be a reality."

He added of Putin: "He wants to scare the whole world. These are the first steps of his nuclear blackmail. I don't think he's bluffing."

Truss told CNN in a September 25 interview: "We should not be listening to [Putin's] saber-rattling and his bogus threats."

"Instead, what we need to do is continue to put sanctions on Russia and continue to support the Ukrainians because if Putin is allowed to succeed, this wouldn't just send a terrible message in Europe and, of course, huge threats to the Ukrainian population themselves, but it also would send a message to other authoritarian regimes around the world that it's somehow acceptable to...invade a sovereign nation."

U.S. officials were less dismissive of the Kremlin threat.

"If Russia crosses this line, there will be catastrophic consequences for Russia; the United States will respond decisively," Sullivan said on U.S. television.

With reporting by Reuters, dpa, and CNN