Secretary General Antonio Guterres urged restraint as Russia accused the US of encouraging "terrorists" in the region with its unilateral actions.
Russia has promised to strengthen Syria's anti-aircraft defences.
In the first direct US military action against Syria's government, at least six people were reported to have been killed after 59 Tomahawk cruise missiles were fired at Shayrat air base in Homs about 4.40am local time from destroyers in the eastern Mediterranean.
US officials said the base was used to launch a chemical weapons attack that killed dozens of civilians on Tuesday.
Idlib's opposition-run health authority said 89 people, including 33 children and 18 women, died in a suspected nerve gas attack in the rebel-held town of Khan Sheikhoun. Syria denies using nerve gas.
The Syrian Observatory for Human Rights said Syrian warplanes had continued taking off from the air base on Friday after the attack, and carried out air strikes on rebel-held areas in the eastern Homs countryside
Russia's deputy ambassador to the UN, Vladimir Safronkov, told Friday's session in New York the US military's "illegitimate" missile strikes had encouraged "terrorists" in Syria.
"We strongly condemn the illegitimate actions by the US. The consequences of this for regional and international stability could be extremely serious," he warned.
"When you take your own path, this leads to horrible tragedies in the region," he said.
US ambassador Nikki Haley said America had acted to ensure President Bashar al-Assad would never use chemical weapons again.
She blamed Iran and Russia for standing by the Syrian government when it committed crimes.
"Strengthening Assad will only lead to more murders," she said.
The UK ambassador, Matthew Rycroft, said the US strikes were a "proportionate response to unspeakable acts".
Russian foreign minister Sergei Lavrov has also described the American offensive as an 'act of aggression', comparing it to the invasion of Iraq in 2003.
Russian Prime Minister Dmitry Medvedev charged that the US strikes were one step away from clashing with Russia's military.
US officials informed Russian forces ahead of the missile strikes, and avoided hitting Russian personnel.
Satellite imagery suggests the base houses Russian special forces and helicopters, part of the Kremlin's effort to help Assad fight Islamic State and other militant groups.
US President Donald Trump has frequently urged improved relations with Russia - which were strained under his predecessor Barack Obama over Syria, Ukraine and other issues - but said action had to be taken against Assad.
- BBC / Reuters