Ukrainian authorities ordered a mandatory evacuation Thursday of nearly 12,000 civilians from 37 towns and villages in the eastern Kharkiv region, where Russian forces reportedly are making a concerted effort to punch through the front line.

The local military administration in Kharkiv’s Kupiansk district said residents must comply with the evacuation order or sign a document saying they would stay at their own risk. Ukraine’s deputy defense minister, Hanna Maliar, had said the previous day that “the intensity of combat and enemy shelling is high” in the area.

The city of Kupiansk and the territories around it were under Russian occupation until September 2022, when Ukrainian forces conducted a rapid offensive operation that dislodged the Kremlin’s forces from nearly the entire Kharkiv region.

The retaking of those areas strengthened Ukraine’s arguments that its troops could deliver more stinging defeats to Russia with additional armament deliveries, which its Western allies provided. But as Ukraine has pursued a slow-moving counteroffensive in recent weeks, Russian forces have struck back in some areas.

Ms. Maliar said Russia “has formed an offensive group and is attempting to move forward” in the area in an effort to advance on the Ukrainian-held city of Kupiansk, an important rail junction.

Russia has concentrated assault troops supported by tank units, aviation and artillery in the Kupiansk area, a Ukraine National Guard spokesman, Ruslan Muzychuk, said on national television.

The Russians have formed eight so-called “Storm-Z” detachments, made up of convicts released from prison acting under military commanders, for the push, and fighting in the area was “intense,” according to the ground forces commander of the Ukrainian Armed Forces, Oleksandr Syrskyi.

Russian media reported that Russian troops had retaken five settlements around Kharkiv, but it was not possible to independently verify either side’s battlefield claims. 

“Some positions are passed from hand to hand constantly,” Mr. Syrskyi said.

Ukrainian authorities have periodically ordered evacuations, especially of children from areas where the fighting has heated up. Officials have previously said the evacuations are necessary to save lives and enable the Ukrainian army to better defend towns from the Russian advance.

Separately, one person was killed and nine injured in a Russian missile strike on the city of Zaporizhzhia late Thursday, said the regional governor, Yuriy Malashko. In Russia, two people died in Ukrainian shelling of the village of Chausi, three miles from the border, said the Bryansk regional governor, Alexander Bogomaz.

Earlier Thursday, Russian air defense systems shot down two drones heading toward Moscow for a second straight day, officials said. The reported attack disrupted flights at two international airports as Ukraine appeared to step up its assault on Russian soil.

One drone was downed in the Kaluga region southwest of Moscow and another near a major Moscow ring road, according to Moscow’s mayor, Sergey Sobyanin, and the Russian Defense Ministry, which blamed the attack on Ukraine.

No casualties or damage were immediately reported.

Domodedovo airport, south of the city, halted flights for more than two hours and Vnukovo airport, southwest of the city, stopped flights for more than two and a half hours, according to Russian news agencies. Ten flights were diverted, Russia’s Federal Agency for Air Transport said.

Firing drones at Moscow after more than 17 months of war has little apparent military value for Ukraine, but the strategy has served to unnerve Russian and bring home to them the conflict’s consequences.

Kyiv officials, as usual, neither confirmed nor denied Ukraine’s possible involvement in the drone strikes, though an Air Force spokesman, Yurii Ihnat, remarked: “This cannot but please us because people in Moscow thought they were safe. Now, the war affects each and every Russian.”

Russia’s Defense Ministry also said it had stopped Ukrainian drone attacks in Moscow-annexed Crime. It said it shot down two drones near the port city of Sevastopol and electronically jammed nine that crashed into the Black Sea.

The Pentagon is to provide Ukraine with another $200 million in weapons and ammunition to help sustain the counteroffensive, according to American officials.

Ukraine has already received more than $43 billion from the U.S. since Russia invaded last year.

As Ukraine’s counteroffensive has stalled, American public support for assistance to the country has slipped. According to a new CNN/SSRS poll, 55 percent of voters say that Congress should not authorize additional funding to support Ukraine. 

It is likely that combat will intensify ahead of the oncoming autumn season, when weather conditions could start to have an adverse impact on troop movements, particularly in eastern Ukraine where most of the fighting has been taking place.