His remarks come as Russia's Wagner mercenary group, which has spearheaded the attack on Bakhmut, claimed to have captured the eastern bank of the industrial town that has been devastated in the longest battle since Moscow invaded.
In Stockholm, EU ministers were discussing plans to ramp up defence production and rush ammunition to Ukraine as it burns through thousands of howitzer shells each day.
Wagner chief and Kremlin ally Yevgeny Prigozhin said on social media Wednesday that his forces "have taken all of the eastern part of Bakhmut", a salt-mining town with a pre-war population of 80,000.
The intense fighting around Bakhmut has been the longest and bloodiest in Russia's more than year-long invasion, which has devastated swathes of Ukraine and displaced millions of people.
"What we see is that Russia is throwing more troops, more forces and what Russia lacks in quality they try to make up in quantity," Stoltenberg told reporters in Stockholm on the sidelines of an EU defence ministers meeting.
"We cannot rule out that Bakhmut may eventually fall in the coming days," the head of the US-led military alliance said, adding that "this does not necessarily reflect any turning point of the war".
Ukrainian President Volodymyr Zelensky warned in an interview with CNN what could happen if Bakhmut falls to Russian forces.
"We understand that after Bakhmut, (Russian forces) could go further" and attack nearby cities in the Donetsk region.
"They could go to Kramatorsk, they could go to Sloviansk, it would be an open road for the Russians after Bakhmut to other towns in Ukraine, in the Donetsk direction," Zelensky said in an interview set to air Wednesday.
Russia aims for 'further offensive'
Russian Defence Minister Sergei Shoigu told military officials during a televised meeting on Tuesday that taking control of the city would allow for "further offensive operations" in eastern Ukraine.
Prigozhin estimated the day before that between "12,000 and 20,000" Ukrainian troops were still defending the town.
Zelensky told CNN that his armed forces were resolved to stay in Bakhmut.
"Of course, we have to think about the lives of our military. But we have to do whatever we can whilst we're getting weapons, supplies, and our army is getting ready for the counter-offensive."
Zelensky on Wednesday hosted UN chief Antonio Guterres in Kyiv as he makes his third visit to Ukraine since Russia's invasion.
In a statement following the talks, Guterres underscored the importance of extending an expiring deal that has allowed Ukraine to export its grain.
"I want to underscore the critical importance of the rollover of the Black Sea Grain Initiative on 18 March," Guterres said.
EU defence ministers were meeting in Stockholm to discuss a plan to rush one billion euros worth of ammunition to Ukraine as pressure mounts on Kyiv's allies to bolster supplies to the war effort.
Ukraine's Western backers warn that Kyiv is facing a critical shortage of 155-millimetre howitzer shells as it fires thousands each day in its fight against the grinding Russian offensive.
"The current rate of consumption compared to the current rate of production of ammunition is not sustainable, and therefore we need to ramp up production," Stoltenberg said.
During a visit to Canada on Tuesday, European Commission President Ursula von der Leyen underscored a European resolve to ward off Russian aggression.
But a report by The New York Times on Tuesday claiming that US officials had seen new intelligence indicating a "pro-Ukrainian group" was behind last year's sabotage of the Nord Stream gas pipelines could raise difficult questions among the allies.
"This is not our activity," Ukraine's Defence Minister Oleksiy Reznikov told reporters in Stockholm.
'Glory to Ukraine'
As Russia said it was closer to capturing Bakhmut, Ukraine identified the man who was shot dead in a video that sparked outrage on social media as one of its soldiers.
The footage shows what appears to be a detained Ukrainian combatant standing in a shallow trench and smoking, and then being shot after saying "Glory to Ukraine".
"Based on a preliminary examination, we believe that the video may be authentic," a spokeswoman for the UN Human Rights Office told AFP on Wednesday.
In Kyiv, Guterres said the "shocking" footage was "yet another tragic reminder that the laws of war must be strictly respected".
Both sides have said the Bakhmut battle has cost a significant number of troops, though neither has given figures.
Ukrainian officials say around 4,000 civilians remain in the town, which has been virtually flattened, including dozens of children.