Pence said Trump was hopeful China "will take actions needed to bring about change in policy" in North Korea.
"But as the president has made very clear, either China will deal with this problem or the United States and our allies will," he said.
Trump's decision to order a cruise missile strike on a Syrian airfield this month, in response to what he said was Syria's use of chemical weapons, raised questions about his plans for reclusive North Korea.
Japanese Prime Minister Shinzo Abe urged North Korea to refrain from taking further provocative actions, comply with U.N. resolutions and abandon its nuclear missile development.
"Japan will closely cooperate with the U.S. and South Korea over North Korea and will call for China to take a bigger role," Abe told parliament.
However, a U.S. foreign policy adviser traveling with Pence sought to defuse some of the tension, saying Sunday's test of what was believed to be a medium-range missile had come as no surprise.
"We had good intelligence before the launch and good intelligence after the launch," the adviser told reporters on condition of anonymity.
China has spoken out against the North's weapons tests and has supported U.N. sanctions. It has repeatedly called for talks while appearing increasingly frustrated with the North.
Beijing banned imports of North Korean coal on Feb. 26, cutting off Pyongyang's most important export. China's customs department issued an order on April 7 telling traders to return North Korean coal cargoes, trading sources said.
Pyongyang has conducted several missile and nuclear tests in defiance of U.N. sanctions, and regularly threatens to destroy South Korea and the United States. North and South Korea are technically still at war because their 1950-1953 conflict ended in a truce, not a treaty.
The North has said it has developed and would launch a missile that can strike the U.S. mainland, but officials and experts believe it is some time away from mastering the necessary technology, including miniaturizing a nuclear warhead.
Sunday's missile launch was a calculated move, the China Daily newspaper said in an editorial.
"And making it without prompting a furious response from Washington surely qualifies as a win to some degree from Kim's perspective," it said, referring to Kim Jong Un.
"Trump, too, can claim a win. That the nuclear test did not happen will surely be seen as the pressure working."