Ukrainian President Volodymyr Zelenskyy welcomed the move but criticised what he called an "unacceptable" delay.
"When over 50 days have passed between the fifth and sixth sanction packages, the situation is not acceptable for us," Mr Zelenskyy said, speaking alongside Slovakian President Zuzana Caputova in Kyiv.
Foreign military analysts say Russia has drained manpower and firepower from across other parts of the front to concentrate on Sievierodonetsk, hoping a massive offensive will achieve one of its stated aims - to secure surrounding Luhansk province for separatist proxies.
"We can say already that a third of Sievierodonetsk is already under our control," Russia's TASS state news agency quoted Leonid Pasechnik, the leader of the pro-Russian Luhansk People's Republic, as saying earlier.
Fighting was raging in the city but Russian forces were not advancing as rapidly as might have been hoped, he said, claiming that they wanted to "maintain the city's infrastructure" and moved slowly because of caution around chemical factories.
A Russian airstrike hit a nitric acid tank, Luhansk governor Serhiy Gaidai said on Tuesday.
In a post on the Telegram app, he urged local residents not to leave bomb shelters because of the risk posed by toxic fumes.
In its evening briefing note on Facebook, Ukraine's military command said that Russian forces were "attempting to take full control of Sievierodonetsk" and surround Ukrainian units fighting there.
"Unfortunately... the city has been split in half. But at the same time the city still defends itself. It is still Ukrainian," the head of the city administration, Oleksandr Stryuk, said, advising those still trapped inside to stay in cellars.
Ukraine says Russia has destroyed all of the city's critical infrastructure with unrelenting bombardment, followed by wave after wave of mass ground assaults involving huge numbers of casualties.
Jan Egeland, secretary general of the Norwegian Refugee Council aid agency which had long operated out of Sievierodonetsk, said he was "horrified" by its destruction.
"We fear that up to 12,000 civilians remain caught in crossfire in the city, without sufficient access to water, food, medicine or electricity," he said.