Backed by China, Pyongyang's main ally, the council agreed on a US-drafted statement describing the test-firing of the missile as a "grave violation" of UN resolutions and threatening "further significant measures."
The council met behind closed doors at the request of the United States, Japan and South Korea after Pyongyang announced it had successfully tested a new missile on Sunday, the first launch since Trump took office.
At a Washington news conference a few hours before the council meeting, Trump described North Korea as a "big, big problem" and vowed "we will deal with that very strongly."
The latest missile was launched from the western city of Kusong and flew east for about 500 kilometers (310 miles) before falling into the Sea of Japan (East Sea), South Korea's defense ministry said.
US Ambassador Nikki Haley called on the council to "use every available resource to make it clear to the North Korean regime – and its enablers – that these launches are unacceptable.
"It is time to hold North Korea accountable – not with our words, but with our actions," she said in a statement.
UN resolutions bar North Korea from carrying out ballistic missile launches or nuclear tests.
But it conducted two nuclear tests and numerous missile launches last year in its quest to develop a nuclear weapons system capable of hitting the US mainland.
No military solution
The Security Council has imposed six sets of sanctions since Pyongyang first tested an atomic device in 2006.
Enforcing those measures is key to changing Pyongyang's behavior, Japan's Ambassador Koro Bessho said, cautioning that "it takes time."
"We need to keep on pushing. We are not looking for a military solution," he said.
"We will have a peaceful solution and the Security Council is the body that is most suited for that," he added.
The US Defense Department warned that the United States and its allies have the capability to shoot down any missile from North Korea.
Pyongyang is "very open and transparent about their desire to build this capability, and we are open about our ability to defeat it," Pentagon spokesman Navy Captain Jeff Davis said.
The United States is also working with Seoul to install a THAAD anti-missile system in South Korea, a move opposed by China.
France also called for ensuring that sanctions are fully implemented.
"It also implies on the European side working towards additional EU measures," French Ambassador Francois Delattre said, without elaborating.
UN Secretary General Antonio Guterres strongly condemned the missile test and had called for a united international response to the "further troubling violation" of UN resolutions.
"The DPRK leadership must return to full compliance with its international obligations and to the path of denuclearization," he said in a statement, referring to North Korea.
China and the United States worked together to draft the two latest UN sanctions resolutions, aimed at curbing North Korea's export revenues and weakening its ability to build up its ballistic and nuclear technology.
New type of weapon system
The North's leader Kim Jong-Un "expressed great satisfaction over the possession of another powerful nuclear attack means which adds to the tremendous might of the country," the state news agency KCNA said on Monday.
It released photos showing the missile blasting into the sky with a smiling Kim watching from the command center and standing on the launch field surrounded by dozens of cheering soldiers and scientists.
The missile was described as a surface-to-surface "medium long range" Pukguksong-2, a "Korean-style new type strategic weapon system."
North Korea claims it has developed an intercontinental ballistic missile (ICBM) capable of hitting the US mainland, but has not yet tested one.
KCNA said the missile tested Sunday was powered by a solid-fuel engine -- which needs a far shorter refueling time than conventional liquid fuel-powered missiles.
The South has said that Sunday's launch was intended as a test for Trump, who responded by pledging "100 percent" support for Washington's key regional ally Japan.
Trump has pressed China to play a bigger role in restraining its wayward neighbor.
China's foreign ministry spokesman Geng Shuang said Beijing opposes North Korean missile launches that violate UN resolutions.
Russia's foreign ministry called the launch "a demonstration of contempt for UN Security Council resolutions."
