(Recasts first two paragraphs to raise North Korean response, U.S. officials praising China)
* U.S. Vice President Pence visits highly fortified DMZ
* Pence's arrival follows failed missile launch by North
* He says Syria, Afghan strikes show U.S. resolve
By Roberta Rampton and Sue-Lin Wong
SEOUL/PYONGYANG, April 17 (Reuters) - U.S. Vice President Mike Pence warned North Korea on Monday that recent American military strikes in Syria and Afghanistan showed President Donald Trump's resolve should not be questioned, but Pyongyang vowed to continue missile and nuclear tests.
After a huge display of missiles in Pyongyang and a failed North Korean missile test during the weekend, U.S. officials praised China for stepping up efforts to rein in North Korea, Beijing's neighbor and ally.
But Pence and South Korea's acting president, Hwang Kyo-ahn, said they would proceed with the early deployment to South Korea of the U.S. THAAD missile-defense system, in spite of Chinese objections.
At a White House Easter celebration on Monday, Trump was asked if he had a message for North Korean leader Kim Jong Un, and replied: “Gotta behave.”
But senior North Korean officials remained defiant.
North Korea's deputy representative to the United Nations, Kim In Ryong, accused Washington of creating “a situation where nuclear war could break out an any time” and said Pyongyang's next nuclear test would take place "at a time and at a place where our headquarters deems necessary."
North Korea's Vice Foreign Minister Han Song-Ryol told the BBC that missiles would continue to be tested on "a weekly, monthly and yearly basis."
Kim Song Gyong, director general of the European Department of North Korea's Foreign Ministry, told Reuters in Pyongyang that if Washington made "the slightest movement" to make a nuclear strike on North Korea, Pyongyang would strike first and "destroy the aggressors without any mercy.”
He went on to clarify that the approach of a U.S. naval strike force led by the nuclear-powered aircraft carrier Carl Vinson to Korean waters would not be considered enough to constitute “the slightest movement”.
Korean tensions have escalated following repeated North Korean missile tests and concerns that Pyongyang may soon conduct a sixth nuclear bomb test in defiance of U.N. sanctions. Washington is increasingly worried about North Korean efforts to develop a nuclear-tipped missile that could hit the U.S. mainland.
Speaking alongside Hwang, Pence said the world had witnessed Trump's resolve in the past two weeks, which saw a U.S. missile attack on a Syrian airfield and the dropping of a powerful non-nuclear bomb on Islamic State in Afghanistan.
"North Korea would do well not to test his resolve or the strength of the armed forces of the United States in this region," Pence said on what was his first stop of a four-nation Asia tour intended to show that Trump is not turning his back on the increasingly volatile part of the world.
Pence, whose father served in the 1950-53 Korean War, visited the North-South border on Monday and said Washington would stand by its "ironclad alliance" with South Korea.
"All options are on the table to achieve the objectives and ensure the stability of the people of this country," he told reporters as tinny propaganda music floated across from the North Korean side of the so-called demilitarized zone (DMZ).
The Trump administration has said that military action remains an option for dealing with North Korea.
But mindful that this would likely trigger massive retaliation and casualties in South Korea and Japan and among U.S. troops there, U.S. officials say the Trump administration's main focus is on tougher economic sanctions to try to get Pyongyang to abandon its weapons programs.
Trump himself, when asked on Monday if he was considering military action, told Fox News Channel he didn't want to "telegraph" his plans like the previous administration.
"We’ll see what happens. I hope things work out well," he said but added that the United States had tried to engage the North Koreans in talks for a long time.
On Sunday, Trump's national security adviser, H.R. McMaster, said that the United States, its allies and China were working on a range of responses to North Korea's latest missile test, citing what he called an international consensus to act.
He indicated Trump was not considering military action for now, despite the dispatch the carrier group.
U.S. officials say tougher sanctions could include an oil embargo, a global ban on North Korea's airline, intercepting cargo ships and punishing Chinese banks doing business with Pyongyang. They say greater Chinese cooperation is vital.
White House spokesman Sean Spicer said China had taken some "very helpful" steps, although it remained to be seen how effective these would be. Asked if Trump had a "red line" on North Korea, Spicer said the president did not believe these worked.
Susan Thornton, acting U.S. assistant secretary of state for East Asia, said Secretary of State Rex Tillerson and China's top diplomat, State Councilor Yang Jiechi, agreed in a phone call on Sunday on the need for strict enforcement of U.N. resolutions and for international action to press Pyongyang "to cease provocative actions and recommit to peaceful denuclearization.”
Thornton said any new North Korean nuclear test "would draw a pretty significant international response."
"We’re definitely not seeking conflict or regime change," she said. "But we are committed to defending our people and our allies should it be necessary.”
Pence is expected to discuss Korean tensions with Japanese Prime Minister Shinzo Abe on Tuesday when he travels to Tokyo for economic talks with Finance Minister Taro Aso. He will also visit Jakarta and Sydney.
His economic discussions will be closely watched to see how hard a line Washington is prepared to take on trade. Trump campaigned on an "America First" platform, and has vowed to narrow big trade deficits with nations like China and Japan.
But Trump has also shown willingness to link trade to other issues, saying he would cut a better trade deal with China if it exerts influence on North Korea.
China has appeared increasingly frustrated with Pyongyang, speaking out against its weapons tests and supporting United Nations sanctions, while repeatedly calling for talks.
China banned imports of North Korean coal, the country's most important export, in February, and Chinese media have raised the possibility of restricting oil shipments to the North.
However, Beijing says the crisis is one between the United States and North Korea.
Chinese Foreign Ministry spokesman Lu Kang said the situation was "highly sensitive, complicated and high risk" and all sides should "avoid taking provocative actions "
Additional reporting by Sue-Lin Wong in Pyongyang, Jack Kim and James Pearson in Seoul, Daniel Trotta in New York, Lucia Mutikani, Caren Bohan, David Brunnstrom, Matt Spetalnick, Lesley Wroughton and Steve Holland in Washington and Michael Martina in Beijing; Editing by Robert Birsel and Alistair Bell