"The risks now are considerable," Foreign Minister Sergei Lavrov told Russia's state television according to a transcript of an interview on the ministry's website.
"I would not want to elevate those risks artificially. Many would like that. The danger is serious, real. And we must not underestimate it."
Lavrov had been asked about the importance of avoiding World War III and whether the current situation was comparable to the 1962 Cuban Missile Crisis, a low point in US-Soviet relations.
Russia had lost its "last hope to scare the world off supporting Ukraine", Ukrainian Foreign Minister Dmytro Kuleba wrote on Twitter after Lavrov's interview. "This only means Moscow senses defeat."
During a visit to Kyiv, US Secretary of State Antony Blinken and Defense Secretary Lloyd Austin promised more military aid for Ukraine.
But Moscow's ambassador to Washington told the United States to halt shipments, warning Western weapons were inflaming the conflict.
Lavrov said: "NATO, in essence, is engaged in a war with Russia through a proxy and is arming that proxy. War means war."
Russia's two-month-old invasion has left thousands dead or injured, reduced towns and cities to rubble, and forced more than five million people to flee abroad.
Moscow calls its actions a "special operation" to disarm Ukraine and protect it from fascists. Ukraine and the West says this a false pretext for an unprovoked war of aggression by President Vladimir Putin.
Russia has yet to capture any of the biggest cities. Its forces were forced to pull back from the outskirts of Kyiv in the face of stiff resistance.
"It is obvious that every day - and especially today, when the third month of our resistance has begun - that everyone in Ukraine is concerned with peace, about when it all be over," President Volodymyr Zelenskiy said late on Monday.
"There is no simple answer to that at this time."
The US State Department on Monday used an emergency declaration to approve the potential sale of $US165 million ($A230 million) worth of ammunition to Ukraine, which could include artillery ammunition for howitzers, tanks and grenade launchers.
The United States is due to host a gathering of more than 40 countries this week for Ukraine-related defence talks that would focus on arming Kyiv, US officials said.
Just weeks ago, the capital Kyiv was a frontline city under curfew and bombardment. Today, the nearest Russian soldiers are hundreds of kilometres away, and normal life is coming back, with Western leaders visiting and diplomats returning.
Blinken said US diplomats would first go to the western city of Lviv and should be back in Kyiv within weeks. Bridget Brink, now US ambassador in Slovakia, will be the envoy.
But war rages on in Ukraine's east and south, where Russia last week launched a massive offensive.
Russia's defence ministry said its missiles destroyed six facilities powering the railways that were used to deliver foreign weapons to Ukrainian forces in the eastern Donbas region.
Russian forces were continuing on Monday to bomb and shell the vast Azovstal steel plant in Mariupol, where fighters are hunkered down in a city ravaged by a siege and bombardment.
Moscow said it was opening a humanitarian corridor to let civilians out of the plant but Kyiv said no agreement had been reached and appealed to the United Nations for help in reaching one.
Ukraine's general staff also reported Russian shelling of its second-biggest city, Kharkiv, in the northeast as well as towns and villages to the south, but said that assaults on three settlements were repelled.