In his comments, Mattis vowed to "Continue to take necessary measures to defend ourselves and our allies" against North Korea, which is working to develop a nuclear-tipped missile capable of hitting the United States.
The Trump administration has come under growing pressure to open negotiations on a temporary freeze on North Korea's nuclear and missile tests in return for reducing the U.S. military footprint in the Korean peninsula, according to American officials and foreign diplomats.
Citing unnamed USA officials, Reuters reports that Pyongyang may have been testing the last stage engine of an ICBM.
After the launch at a military test site on the southwest coast, Moon said it was important for South Korea to maintain military capability that could "dominate" North Korea in order to maintain peace on the peninsula and for future engagement policies with the North to be effective, his spokesman Park Soo-hyun said.
It's unclear whether the tweet was setting up a change in how the United States deals with North Korea.
The United States has tried for years to discourage South Korea from developing longer-range ballistic missiles in keeping with the Missile Technology Control Regime, a voluntary global arms-control pact.
South Korea's military plans to deploy the Hyunmoo-2 missile after conducting two more tests.
Moon told Reuters in an exclusive interview on Thursday that strong new sanctions would be needed if the North conducted a new nuclear test or an intercontinental ballistic missile test and that he planned to call on Chinese President Xi Jinping to play a greater role in reining in Pyongyang's arms program. "There are more people and more cars but nobody knows what that means", said the official.
South Korea's news agency says Pyongyang is willing to place a conditional moratorium on the programs if the US agrees to stop joint military drills with the South.
"We have come to a stalemate when it comes to North Korea", she said in response to a question from news.com.au.
A North Korean taekwondo demonstration team has arrived in South Korea for its first performances in the rival country in 10 years. However, during the campaign, Trump was largely spared criticism from North Korea - in one instance, a state media outlet praised him as "wise". ICBMs have a minimum range of about 3,400 miles (5,500 km), but some are created to travel 6,200 miles (10,000 km) or farther.
South Korea's new President Moon Jae-in said Seoul has no plans to scale back joint military exercises with Washington, according to an interview with USA broadcaster CBS.