ZAPORIZHZHIA, Ukraine — With winter about to set in, Russia and Ukraine are locked in heavy exchanges of fire across the front line in increasingly urgent attempts to make gains big or small while they still can.
Attacks flared in the Sumy region in the north, where rockets and mortars hit at least six settlements on Saturday, half a year after Russian forces withdrew from the area. And in Russian-occupied areas of the south, Ukrainian forces struck targets, among them a hotel used by Russian officials and local collaborators.
“It was loud again in Enerhodar,” the town’s mayor, Dmytro Orlov, who is in exile, said in a post on the Telegram messaging app alongside a photo of a burning building.
Both sides in the south have been striking deep behind each other’s lines, but in recent days, the battlefield positions have not appeared to move much. In other parts of the country, Russian cruise missiles and drones struck across Ukrainian territory, as Moscow’s campaign to cripple Ukraine’s energy supplies continued.
After months of no contact, the two top American and Russian military officials held their second discussion in three days. The phone call on Sunday between Defense Secretary Lloyd J. Austin III and Defense Minister Sergei K. Shoigu was intended to make clear the red lines that might provoke Russia to launch a nuclear attack in Ukraine.
Mr. Austin said in a post on Twitter, “I rejected any pretext for Russian escalation & reaffirmed the value of continued communication amid Russia’s unlawful & unjustified war against Ukraine.”
Russia’s Defense Ministry confirmed that the two men spoke, but said only that they had discussed the situation in Ukraine. Mr. Austin and Mr. Shoigu previously spoke on Friday at the initiation of the Pentagon, and in May.
The conversation with Mr. Austin on Sunday was among a flurry of calls that Mr. Shoigu held with his British, French and Turkish counterparts. The calls occurred as a Russian retreat from the Kherson region looked imminent and as Ukrainian forces fought off Russian attacks in several places over the weekend.
Rocket and artillery fire killed eight people and wounded 19 on Saturday, Ukrainian officials reported. Two died in strikes in the Zaporizhzhia region and six in strikes in Donetsk. Russia also unleashed widespread attacks on power plants and heating stations in what Ukraine said were some of the heaviest strikes in weeks.
“The geography of this new massive strike is very wide,” President Volodymyr Zelensky of Ukraine said in his address on Saturday evening.
With the government estimating that 1.5 million households were without power, Mr. Zelensky urged those Ukrainians who still have electricity to use it sparingly and prepare for blackouts.
Small steps that had been made toward easing the conflict seemed in question this weekend, including the internationally brokered agreement to free up tons of desperately needed Ukrainian grain for transport around the world.
On Sunday, Ukraine’s Infrastructure Ministry again accused Russia of deliberately slowing grain exports to stymie the agreement, signed in July, that allowed Ukrainian agricultural exports by sea to resume over the summer.
Russian interference has left Ukraine’s three open ports operating at less than a third of normal capacity, the ministry said on Sunday in a statement on Facebook. The Kremlin has not responded to Ukraine’s accusations.
Ukraine wants the deal extended, but Russia has threatened to refuse, saying the West was not removing the “logistic sanctions” to open up markets to its grain and fertilizer. Mr. Zelensky says there is a backlog of 150 ships waiting to fulfill contracts to transport Ukrainian wheat, corn, sunflower oil and other products.
“This is an artificial queue,” he said. “It arose only because Russia is deliberately delaying the passage of ships.”
Ismini Palla, a spokeswoman for the United Nations group overseeing the agreement, confirmed the backlog, but declined to comment on what was causing it. She said a team of officials from Russia, Turkey, Ukraine and the United Nations “has acknowledged this problem and is trying to address the backlog.”
Mr. Austin’s conversation with the Russian defense minister, which took place at 7:30 a.m. Eastern on Sunday, was meant to clarify for the Biden administration why President Vladimir V. Putin of Russia has been increasingly raising the specter of a nuclear strike in Ukraine, two officials said.
With his forces on the back foot there, Mr. Putin has sought to portray territory in Ukraine he illegally annexed as part of “Mother Russia,” saying any American-backed attack in those areas would be viewed as an attack on Russia.
In the talks with his British, French and Turkish counterparts, Mr. Shoigu also raised concerns about what he claimed was the possibility that Ukraine would use a “dirty bomb” — a conventional explosive laced with radioactive material — according to Russia’s Defense Ministry.
Russia publicly offered no evidence to back up its claims, and the accusations drew a swift and fierce response from Ukrainian and Western officials.
Ukraine’s foreign minister, Dmytro I. Kuleba, called them “lies” that were “as absurd as they are dangerous.” He wrote on Twitter, “We neither have any ‘dirty bombs,’ nor plan to acquire any.”
The White House called Mr. Shoigu’s claims “transparently false.” Britain’s defense ministry similarly rebutted the claims.
In the Donetsk region, Russian troops have made concerted assaults on the towns of Bakhmut and Avdiivka, the Ukrainian military command said Saturday evening. The two towns have long been at the center of fighting as Russia has sought to extend its control of the region, with Ukrainian troops putting up dogged resistance.
But in Kherson, the southern city where Moscow’s position has become increasingly precarious, there were signs that Russian forces have started to move out military equipment, Ukrainian officials said.
Kherson, a major industrial port city on the west bank of the Dnipro River, was captured early in the war and is the capital of one of the regions illegally annexed by Russia. But for weeks, Ukrainian forces have been inching toward Kherson, village by village. They have also bombed the main road bridges close to the city, making it harder for Russia to resupply its troops.
Over the weekend, Moscow-installed officials urged residents to use boats to cross the river and move farther into Russian-held territory. Kyiv has dismissed the relocation effort as “a propaganda show” intended to scare civilians with claims that Ukraine would shell the city, but some analysts said there could be other motives.
The Institute for the Study of War, a Washington-based research organization, noted on Saturday that Russian-backed officials had urged people who were leaving to bring clothes, valuables and documents, suggesting they did not expect a quick return.
It said the Russians were probably trying to “depopulate” parts of the Kherson region that Ukraine would recapture, “damaging the long-term social and economic viability of southern Ukraine.”
Carlotta Gall reported from Zaporizhzhia, Ukraine, Helene Cooper from Washington and Eric Nagourney from New York. Oleksandr Chubko contributed reporting from Zaporizhzhia, Matt Surman from London and James C. McKinley Jr. from New York.