(Adds analyst comment, human rights group quote)
* Trump says would meet N.Korean leader under right circumstances
* Comment draws criticism in Washington
* White House says conditions 'not there right now'
* North Korea suggests it will continue nuclear tests
* Pyongyang says it will bolster force "to the maximum"
* Tension high with U.S. aircraft carrier group in the region
By Ayesha Rascoe and Soyoung Kim
WASHINGTON/SEOUL, May 1 (Reuters) - U.S. President Donald Trump on Monday opened the door to meeting North Korea's Kim Jong Un, saying he would be honored to meet the young leader under the right circumstances, even as Pyongyang suggested it would continue its nuclear weapons tests.
“If it would be appropriate for me to meet with him, I would absolutely, I would be honored to do it,” Trump told Bloomberg News, comments that drew criticism in Washington.
"Under the right circumstances I would meet with him," Trump said.
Trump did not say what conditions would need to be met for any such meeting to occur or when it could happen, but the White House later said North Korea would need to meet many conditions before a meeting could be contemplated. "Clearly conditions are not there right now," White House spokesman Sean Spicer said.
"I don’t see this happening anytime soon," Spicer added.
Trump, who took office in January, had said during his presidential campaign he would be willing to meet with Kim.
His administration has since said North Korea must agree to abandon its nuclear and missile programs and has sought to pressure Pyongyang economically and diplomatically while insisting that military options remain "on the table."
On Friday, U.S. Secretary of State Rex Tillerson told the United Nations Security Council that Washington would not negotiate with North Korea. U.S. Vice President Mike Pence, earlier on Monday, said Trump had made clear "that the era of strategic patience is over."
Later on Monday, a U.S. State Department spokeswoman said in a statement: “The United States remains open to credible talks on the denuclearization of the Korean peninsula; however conditions must change before there is any scope for talks to resume,” adding that North Korea must abandon its nuclear weapons program.
Despite that, Trump's statement that he would be "honored" to meet Kim - as well as his description of the young North Korean leader over the weekend as "a pretty smart cookie" - sparked fresh concern over his approach to North Korea.
"I don't see much coherence in the Trump administration's statements," said Bonnie Glaser, an Asia expert at the Center for Strategic and International Studies in Washington. "If there is to be any hope of getting Kim Jong Un back to the negotiating table to discuss denuclearization, the U.S. has to articulate a clear position."
John Sifton, Asia director for Human Rights Watch, said Trump had established a troubling pattern of paying compliments to foreign leaders with shaky human rights or autocratic reputations. "You don't have to be a psychologist to see that he admires leaders who ignore the rule of law," he said.
Tensions on the Korean peninsula have been high for weeks, driven by fears the North might conduct a long-range missile test, or its sixth nuclear test, around the time of the April 15 anniversary of its state founder's birth.
Early on Monday, North Korea said it would bolster its nuclear force "to the maximum" in a "consecutive and successive way at any moment" in the face of what it calls U.S. aggression and hysteria.
North Korea, technically still at war with the South after their 1950-53 conflict ended in a truce, not a treaty, regularly threatens to destroy the United States, Japan and South Korea and has said it will pursue its nuclear and missile programs to counter perceived U.S. aggression.
Trump warned in an interview with Reuters on Thursday that a "major, major conflict" with North Korea was possible , while China said last week the situation on the Korean peninsula could escalate or slip out of control.
In a show of force, the United States has sent the nuclear-powered USS Carl Vinson aircraft carrier group to waters off the Korean peninsula to join drills with South Korea to counter a series of threats of destruction from North Korea, formally known as the Democratic People's Republic of Korea (DPRK).
"Now that the U.S. is kicking up the overall racket for sanctions and pressure against the DPRK, pursuant to its new DPRK policy called 'maximum pressure and engagement', the DPRK will speed up at the maximum pace the measure for bolstering its nuclear deterrence," a spokesman for North Korea's foreign ministry said in a statement carried by its official KCNA news agency.
North Korea's "measures for bolstering the nuclear force to the maximum will be taken in a consecutive and successive way at any moment and any place decided by its supreme leadership," the spokesman said.
Reclusive North Korea has carried out five nuclear tests and a series of missile tests in defiance of U.N. Security Council and unilateral resolutions. It has been conducting tests at an unprecedented rate and is believed to have made progress in developing intermediate-range and submarine-launched missiles.
It test-launched a missile on Saturday which Washington and Seoul said was unsuccessful but which nevertheless drew widespread international condemnation.
SOUTH KOREAN MISSILE DEFENSE
Separately, South Korea said the United States had reaffirmed it would shoulder the cost of deploying the Terminal High Altitude Area Defense (THAAD) anti-missile system to counter the North Korean threat, days after Trump said Seoul should pay for the $1 billion battery.
In a telephone call on Sunday, Trump's national security adviser, H.R. McMaster, reassured his South Korean counterpart, Kim Kwan-jin, that the U.S. alliance with South Korea was its top priority in the Asia-Pacific region, the South's presidential office said.
The THAAD system in South Korea has reached an initial operating capability to defend against North Korean missiles, U.S. officials said on Monday. It would not be fully operational for some months, however, one of them cautioned.
The THAAD deployment has drawn protests from China, which says the powerful radar that can penetrate its territory will undermine regional security, and from residents of the area in which it is being deployed, worried they will be a target for North Korean missiles.
Over the weekend, Trump stepped up his outreach to allies in Asia to discuss the North Korean threat.
As part of that effort, he invited Philippines President Rodrigo Duterte to meet in Washington, a move human rights organizations condemned but which the White House defended as necessary for countering North Korea.
Washington is also seeking more help from China, the North's only major ally, to rein in Pyongyang's nuclear and missile development. Unlike the United States, Beijing has pushed for talks first and action later on North Korea.
"The United States has ... negotiated, had talks, waited patiently. All the while we've seen the regime in North Korea continue its headlong pursuit of nuclear weapons, and a ballistic missile program. And the president said that's over," Pence told CBS News in an interview.
(Additional reporting by Matt Spetalnick, David Brunnstrom, Phil Stewart and Idrees Ali in Washington; Writing by Nick Macfie, Soyoung Kim and Susan Heavey; Editing by Robert Birsel, James Dalgleish and Jonathan Oatis)