Moon said the missile test violates UN Security Council resolutions and called it a severe challenge to the peace and security of the Korean Peninsula and the world, presidential spokesman Yoon Young-chan said.
South Korea needs to show the North that even though talks are possible, it will only be possible if North Korea changes its attitude, the President told staff at the meeting.
He said South Korea will respond to provocations.
The direction of the missile, so close to Russia, was likely an attempt by North Korean leader Kim Jong Un to send a message to both Moscow and Beijing, said Carl Schuster, a Hawaii Pacific University professor and former director of operations at the US Pacific Command's Joint Intelligence Center.
"It tells Russia, 'I can touch you too,'" Schuster said.
"It tells China, 'I don't care what you think, I'm independent,'" he said.
China remains one of North Korea's only allies and is responsible for much of the heavily-sanctioned nation's economy.
On Sunday, Chinese leader Xi Jinping launched a major trade and infrastructure summit with multiple world leaders in Beijing. Russian President Vladamir Putin as well as a North Korean delegation attended the conference.
"The timing is not coincidental," Schuster said, adding that Kim may be trying to get Putin more involved on the situation on the Korean Peninsula.
"It's his way of telling the Russians, 'You need to speak up,'" and stop US-supported international sanctions on North Korea, Schuster said.
The United States called for repercussions from the international community.
"Let this latest provocation serve as a call for all nations to implement far stronger sanctions against North Korea," White House press secretary Sean Spicer said in a statement.
700-kilometer flight
The missile, launched near the city of Kusong, flew 700 kilometers (435 miles), the South Korean military said. A US defense official confirmed that it flew that far, but said the US was still investigating to determine the type of missile.
"At this point, we see nothing consistent with an (intercontinental ballistic missile) launch," a second defense official told CNN.
Condemnation from Japan
Japanese Prime Minister Shinzo Abe condemned the launch in a quick doorstep interview with reporters.
"Despite strong warning from the international community, North Korea launched a ballistic missile again," Abe said. "This is totally unacceptable and we strongly protest it. North Korea's missile launch is a serious threat to Japan and clearly violate against the UN resolution."
Chief Cabinet Secretary Yasuhide Suga said the government didn't initiate a "J alert," a nationwide alert system for missile launches. He added that the missile didn't come down in Japan's exclusive economic zone, waters within 322 kilometers (200 miles) of the coast for which it has jurisdiction over resources.