The US Navy dispatched the aircraft carrier USS Carl Vinson strike group to the region last weekend, and Trump has been tweeting this week that if China can't rein in North Korea's nuclear program, the United States will.
Mr. Pence told reporters during a surprise visit Monday to the Demilitarized Zone (DMZ) between North and South Korea that President Trump is hopeful that China will use their "extraordinary levers" to pressure the North to abandon their weapons.
Pence made an unannounced visit to the Demilitarized Zone Monday at the start of his 10-day trip to Asia in a US show of force that allowed the vice president to gaze at North Korean soldiers from afar and stare directly across a border marked by razor wire. In a statement, Defense Secretary Jim Mattis said Trump and his military team "are aware of North Korea's most recent unsuccessful missile launch".
Lu said Beijing wants to resume the multi-party negotiations that ended in stalemate in 2009 and suggested that US plans to deploy a missile defense system in South Korea were damaging its relations with China.
The United States, which last week acted unilaterally in ordering a cruise missile strike on Syria, has recently dispatched what Trump called an "armada", including an aircraft carrier, into waters off the Korean Peninsula.
In brief remarks to reporters, Mr. Pence praised the "unshakable bond" between the US and South Korea.
Mr Trump said China was "working with us" on the issue - the first confirmation the two nations were collaborating.
The White House believes that Sunday's test involved a medium-range ballistic missile that failed within 4-5 seconds after launch, and that it did not involve an intercontinental ballistic missile, the foreign policy adviser said.
This is the first time we have seen missile canisters of this size and design in North Korea.
Both Japan and South Korea are firmly in the firing line and will want to caution against any United States military action that could prompt a broader conflagration.
Pence, who has called the North's failed missile test a day earlier "a provocation", said the USA and its allies will achieve its objectives through "peaceable means or ultimately by whatever means are necessary" to protect South Korea and stabilize the region.
Urging strategic patience, she explained: "It's like your kids in the back of the vehicle on a long trip saying, 'When are we going to get there?' Well, in this case, I think we should give the Chinese president some opportunities and some time, as well as pursuing the economic and diplomatic pressures that we have and that our allies have that we can bring to bear on North Korea".
South Korean and USA intelligence officials were trying to determine what type of missile was used.
After visiting the DMZ, Pence is expected to hold talks with South Korea's Acting President Hwang Kyo-Ahn in Seoul. She advised patience with China on the issue.
"Either China will deal with this problem or the United States and its allies will", Pence said on Monday.
The reported failed test comes at a time of year when North Korea has previously tried to launch missiles.
In Seoul, Pence will try to steer clear of South Korea's tumultuous domestic politics ahead of elections next month.
Along with the deployment of the USA aircraft carrier and other vessels into waters off the Korean Peninsula, thousands of US and South Korean troops, tanks and other weaponry were deployed last month in their biggest joint military exercises.
That test also failed, as there was "no evidence the missile reached flight", a U.S. official told CNN.
Despite all the displays on Saturday, analysts cautioned against overreaction, noting that North Korea's missile tests have had a checkered record of success, and adding that a missile in a parade does not necessarily mean it's operational. Recent satellite imagery suggests the country could conduct another underground nuclear test at any time.