The General Staff of the Ukrainian military said 34 combat clashes took place on the front line during the day on September 7 and that the situation in the east and south of Ukraine "remains difficult."
The Ukrainian military repelled attacks in the Kupyansk, Bakhmut, and Avdiyivka areas, it said in its evening assessment.
"The Defense Forces of Ukraine continue to conduct an offensive operation in the Melitopol direction, destroy the enemy, and step-by-step liberate the occupied territories," it reported.
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A late air strike on Nikopol in the Dnipropetrovsk region wounded two people after constant shelling of the region throughout the day, regional Governor Serhiy Lysak said.
Lysak said the injured -- a 52-year-old woman and a 57-year-old man -- suffered shrapnel wounds. A house caught fire and several others were damaged, he said. Russian shelling of another community, Pokrovsk, resulted in a fire, he said.
The attacks came as the U.S. Defense Department announced a new security-assistance package to support Ukraine's battlefield needs. The package is valued at up to $600 million and includes equipment to augment its air defenses, artillery munitions, and other capabilities, the Pentagon said in a statement.
The equipment will be procured from defense contractors as opposed to drawn from existing stockpiles and therefore not likely to arrive on the battlefield anytime soon.
Ukraine's military reported shooting down 25 of the 33 drones it said were launched by Russia. Most were aimed at the Odesa region but some also targeted the northern area of Sumy, it added.
Ukrainian port infrastructure in Izmayil was damaged earlier on September 7 in another Russian drone attack. A grain silo and administrative buildings were damaged in the attack on the Danube River port southwest of Odesa, said Oleh Kiper, the governor of the Odesa region.
One person was injured in the attack, the fourth on a key Danube River port in the last five days, he said.
Russia has stepped up attacks on Ukraine's grain-export infrastructure amid talks about the resumption of the Black Sea grain deal that would allow unhindered exports of grain from Ukrainian ports.
Russia quit the deal in July, a year after it was brokered by the United Nations and Turkey.
Ukrainian President Volodymyr Zelenskiy said on X, formerly Twitter, that he had a conversation with British Prime Minister Rishi Sunak about Black Sea grain exports.
"Ukraine has successfully opened an alternative path and needs the help of partners in strengthening the air defense of Odesa," Zelenskiy said.
In his evening address, he said Ukraine had "a few very practical goals" for its cooperation with partners in September. These involve new weapons, new diplomatic efforts to unite more countries around the goal of restoring a just peace, and new pressure on Russia.
In Russia, drones were downed near Moscow, the southern Rostov region, and the Bryansk regions in the southwest, state media quoted Russian authorities as saying.
According to TASS, three buildings were damaged in the city of Rostov-on-Don, a city of 1 million people nearly 1,000 kilometers south of Moscow. It is also home to Russia's Southern Military District. One explosion was reported near its headquarters.
Vasily Golubev, governor of the Rostov region, said one person was injured when one of the drones crashed in the downtown area.
In the Moscow region, a drone was downed over the town of Ramenskoye, southeast of the Russian capital, according to Moscow Mayor Sergei Sobyanin.
In Bryansk, a Ukrainian drone targeted an industrial site late on September 7, setting an administrative building on fire but causing no injuries, Governor Aleksandr Bogomaz said on Telegram. Emergency services were dispatched to the scene, he said.
The fresh drone strikes come a day after 17 people were killed and dozens wounded in a Russian missile strike on a busy outdoor market in the eastern Ukrainian city of Kostyantynivka, near the front line in the Donetsk region.
"Those who know this place are well aware that it is a civilian area," President Volodymyr Zelenskiy said. "There aren't any military units nearby. The strike was deliberate."
PHOTO GALLERY: An Associated Press photographer captured the horrific scene following a deadly Russian missile attack that struck a busy market in the center of Kostyantynivka, in eastern Ukraine, on September 6. WARNING: This gallery contains graphic content.
Aftermath Of Deadly Missile Strike At Market In Ukraine's Kostyantynivka
An eyewitness of the Russian missile attack on the busy market told RFE/RL's Ukrainian Service that cars and market stalls caught fire after the explosion, which sent people running in all directions in a scene of mass confusion and fear.
"This is the market. There were a lot of people. The market is lively," the eyewitness said. "It's very difficult for us. We ask the whole world to stop this war. We're tired. We are old people."
Ukraine is in the third month of a major counteroffensive against Russian forces that it hopes will decisively shift the momentum of the war.
The pace of the counteroffensive has been criticized by some politicians and observers in the West, but a former U.S. diplomat who spoke in Kyiv on September 7 said these critics had the wrong expectations.
Former U.S. special envoy Kurt Volker said Ukrainian forces were attacking in many places along the front line so that Russia is forced to stretch its forces out. Where possible, Ukrainian forces then push through. He said Ukrainian forces were also successfully disrupting Russian supply lines in the occupied territories, particularly Crimea and southern Ukraine.
Volker said Ukraine had hit fuel and ammunition depots, bridges, and roads and used drones to target Russian Navy ships, disrupt Russian oil supplies, and force commercial air traffic in Russia to halt, "bringing the reality of this war to the Russian people."