UN envoy Maman Sidikou said threats to the 18,000-strong peacekeeping mission there outstripped its capabilities.
Violent protests have broken out over the postponement of presidential polls.
The opposition accuses President Joseph Kabila of trying to cling to power beyond the end of his term, which is due to expire in December.
Dozens of people died in anti-government violence in the capital Kinshasa last month after the electoral commission said it could not hold polls in November.
The headquarters of three opposition parties were also attacked and burned down.
“Actors on all sides appear more and more willing to resort to violence to achieve their ends,” Mr Sidikou, head of the UN peacekeeping mission known as MONUSCO, told the UN Security Council on Tuesday.
“While MONUSCO will do everything it can within its mandate to protect civilians, the scope of the threats dramatically outstrip the mission’s capabilities.”
He added: “The Democratic Republic of Congo has entered a period of extreme risk to its stability. The coming period will certainly be extremely difficult, the tipping point in the serious violence could be reached very quickly.”
DR Congo has never had a smooth transfer of power since independence more than 55 years ago.
Mr. Kabila took power in 2001 following the assassination of his father, Laurent Kabila, and the constitution bars him from running for office again.
Last month, the US imposed sanctions on two senior security officials allied to President Kabila.
It accused army Gen. Gabriel Amisi Kumba and John Numbi, a former police chief, of threatening the country’s stability by suppressing the opposition.
A government-backed effort to work out a solution to the political crisis, called a “national dialogue”, has been boycotted by most opposition parties.