The situation in Bakhmut, on Ukraine's eastern frontline, is becoming "more and more difficult," according to Ukraine's President Volodymyr Zelensky.
For over six months, Russian forces have been attempting to take the city.
"The enemy is constantly destroying everything that can be used to defend our positions," said Mr Zelensky.
During a visit to Kyiv on Monday, US Treasury Secretary Janet Yellen warned China against arming Russia.
Some of the fiercest fighting since Russia's invasion of Ukraine just over a year ago has taken place in Bakhmut, in Ukraine's Donetsk region, which is controlled by Russia and its separatist allies.
Russian forces' efforts to capture the industrial city have recently intensified, with their troops gaining ground.
The separatist leader of the self-proclaimed Donetsk People's Republic, Denis Pushilin, said "practically all roads" into the city were "under [Russian] fire control."
And the commander of Ukraine's ground forces, Col. Gen. Oleksandr Syrskyi, said the situation around Bakhmut was "extremely tense."
"Despite significant losses, the enemy threw in Wagner's most prepared assault units, which are attempting to break through our troops' defenses and surround the city," Gen. Syrskyi said.
In his nightly address, President Zelensky stated that gaining a foothold in Bakhmut and ensuring its defense were being severely jeopardized by Russia's renewed onslaught.
He expressed gratitude to "everyone who is heroically holding" the area.
President Zelensky also called once again for modern combat aircraft to be sent so that "the entire territory of our country" can be defended from "Russian terror."
Janet Yellen announced the latest transfer of $1.25 billion (£1 billion) in economic and budget aid to Ukraine during a surprise visit to Kyiv on Monday.
Yellen reiterated US President Joe Biden's message, delivered during his own visit to Kyiv last week, that Washington would stand by Ukraine until the war was won.
Yellen told CNN that while Russia's economy had not yet buckled under the massive sanctions imposed by Western powers, she expected it to weaken over time.
She also stated that Russia's ability to replenish military equipment destroyed in Ukraine attacks was "gradually jeopardized," and that any move by China to supply such weaponry to Russia would have "severe" consequences.
"We have been very clear that we will not tolerate systematic violations of the sanctions that we have put in place to deny Russia access to military equipment to wage this war," she said.
"And we have made it clear to the Chinese government, Chinese firms, and Chinese financial institutions that the consequences of violating those sanctions would be severe."
Last week, US Secretary of State Antony Blinken stated that China was considering supplying Russia with weapons and ammunition. Beijing categorically denied the claim.
A meeting last week in Moscow between China's top diplomat, Wang Yi, and Russia's President Vladimir Putin appeared to many to be an indication of China's close ties with Russia.
And Putin's close ally, Belarusian President Alexander Lukashenko, is set to begin a three-day visit to China on Tuesday. He is expected to meet with President Xi Jinping during his visit.