KYIV, Ukraine — Ukrainian troops are locked in intense battles with the advancing Russian army in two border areas, President Zelensky says, as President Putin’s selection of a new defense chief suggests the Kremlin is aiming to intensify its military onslaught against its neighbor.

Mr. Zelensky says “fierce battles” are taking place near the border in eastern and northeastern Ukraine as outgunned and outnumbered Ukrainian soldiers try to push back a significant Russian ground offensive.

“Defensive battles are ongoing, fierce battles, on a large part of our border area,” Mr. Zelensky said in his nightly video address Sunday.

The Russian push comes as Mr. Putin proposes Andrei Belousov to become the country’s defense minister in place of Sergei Shoigu. Mr. Belousov, 65, has held leading positions in the finances and economic department of the prime minister’s office and the Ministry of Economic Development.

Mr. Shoigu was widely seen as a key figure in Putin’s decision to send Russian troops into Ukraine in February 2022. Russia had expected the operation to quickly overwhelm Ukraine’s army and for Ukrainians to broadly welcome Russian troops.

Mr. Belousov’s appointment raises the prospect that Mr. Putin envisions a broader economic mobilization of Russia with the aim of, far from backing down in his invasion of Ukraine, extending and intensifying his effort to conquer the neighboring country.

The Kremlin’s forces are aiming to exploit Ukrainian weaknesses before a big batch of new military aid for Kyiv from America and European partners arrives on the battlefield in the coming weeks and months, analysts say. 

That makes this period a window of opportunity for Moscow and one of the most dangerous for Kyiv in the two-year war, they say.

The new Russian push in the northeastern Kharkiv region, along with the ongoing drive into the eastern Donetsk region, come after months when the about 620-mile front line barely budged. In the meantime, both sides have used long-range strikes in what largely became a war of attrition.

The Kharkiv incursion may be an attempt to create a “buffer zone” to protect Belgorod, an adjacent Russian border region battered by Ukrainian attacks.

Russian emergency services on Monday finished clearing the rubble in the region’s capital city of Belgorod, where a section of a residential building collapsed following what authorities said was Ukrainian shelling.

Fifteen bodies were pulled from the rubble, Belgorod’s regional governor, Vyacheslav Gladkov, said, and 27 other people were wounded.

Another three people in the city of Belgorod were killed by shelling late Sunday, he said.

Mr. Zelensky said fighting in the Donetsk area is “no less intense” than in Kharkiv. He said the Kremlin aimed to “spread our forces thin” by opening a second active front in Kharkiv.

He described the area around Pokrovsk region, just inside the Ukrainian border in Donetsk, as “the most difficult.”

Pokrovsk was a town of around 60,000 people before the war and was until recently a two-hour drive from the front line. Now it is less than half that.

The capture of the Donetsk city of Avdiivka in February opened a door for the Kremlin’s troops to push westward, deeper into Donetsk. 

Russia illegally annexed Donetsk and three other regions in 2022 shortly after it invaded Ukraine, and taking control of all of Donetsk is one of the Kremlin’s main war goals.