* Talks to follow North Korea test warning; missile launches
* North Korea high on agenda for Obama's Asia visit this month
* US seeking to ease friction, encourage cooperation between allies (Recasts with details of North Korean warnings)
WASHINGTON, April 3 (Reuters) - The United States, Japan and South Korea will meet next week to seek ways to persuade North Korea to give up its atomic weapons program, the U.S. State Department said on Thursday, just days after Pyongyang warned of a "new form" of nuclear test.
The talks next Monday in Washington will follow on from a trilateral summit involving the United States and its two main Asian allies hosted by President Barack Obama in The Hague on March 25.
The discussions precede a visit to Asia by Obama from April 22, which will include stops in both Japan and South Korea, where the North Korea issue will be high on the agenda.
North Korea test-launched two ballistic missiles as the talks in The Hague got underway and on Sunday, after members of the U.N. Security Council criticized that move, Pyongyang said it would not rule out conducting "a new form of nuclear test."
The Washington meeting will be hosted by the U.S. Special Representative for North Korea Policy Glyn Davies.
South Korea will be represented by its Special Representative for Korean Peninsula Peace and Security Affairs Hwang Joon-kook and Japan by its Foreign Ministry's Director General for Asian and Oceanian Affairs Junichi Ihara, it said.
"These discussions reflect the close cooperation among our three countries and our continued focus on pursuing the verifiable denuclearization of the Korean Peninsula in a peaceful manner, the State Department said in a statement.
Last month's talks in The Hague saw the first face-to-face meeting between Japanese Prime Minister Shinzo Abe and South Korean President Park Geun-hye. The North Korean missile launch underscored the need for Washington's two key Asian allies to repair their strained ties.
The United States wants to strengthen the allies' combined response to concerns such as North Korea's banned nuclear weapons program and China's growing assertiveness in disputed Asian waters.
FRICTION BETWEEN ALLIES
Relations between Seoul and Tokyo are clouded by the legacy of Japan's 1910-1945 colonial rule of the Korean peninsula and Seoul's concerns that Abe wants to rewrite Japan's wartime past with a less apologetic tone.
Park, Abe and Obama emphasized the need to work together on containing the North Korean nuclear threat.
On Monday, North Korea fired more than 100 artillery rounds into South Korean waters as part of a drill, prompting the South to fire back, officials in Seoul said, but the exercise appeared to be more saber-rattling from Pyongyang rather than the start of a military standoff.
North Korea had flagged its intentions to conduct the exercise in response to U.N. condemnation of last week's missile launches by Pyongyang and against what it says are threatening military drills in South Korea by U.S. forces.
In its warning about a new nuclear test, North Korea said military drills to counter the United States would involve "more diversified nuclear deterrence" to hit medium- and long-range targets "with a variety of striking power".
North Korea has forged ahead with its nuclear development after declaring so-called six-party talks with world powers aimed at ending its atomic weapons program dead in 2008.
It threatened nuclear strikes against South Korea and the United States last year after the United Nations tightened sanctions against it for conducting a third nuclear detonation since 2006.
Russia and China both expressed concern on Monday about North Korea's threat that it could carry out more nuclear tests.
Most analysts do not believe North Korea has the capability to deliver a nuclear strike on the mainland United States. (Reporting by David Brunnstrom; editing by Andrew Hay)