North Korea's claim to have tested its first hydrogen bomb is the latest foreign policy litmus test in the presidential race: Republican candidates are blaming President Barack Obama's policies for the rogue regime's boldness and seeking to tie the U.S. approach to Democratic presidential frontrunner Hillary Clinton, who served as Obama's secretary of state.

"If this test is confirmed, it will be just the latest example of the failed Obama-Clinton foreign policy," Florida Senator Marco Rubio said in a statement. "Our enemies around the world are taking advantage of Obama's weakness. We need new leadership that will stand up to people like Kim Jong-un and ensure our country has the capabilities necessary to keep America safe."

Former Florida Governor Jeb Bush said on Twitter that North Korea's move shows the danger of continuing the "feckless Obama/Clinton foreign policy."

Carly Fiorina called the development "yet another Hillary Clinton foreign policy failure" in a posting on Facebook and suggested North Korea was emboldened by the U.S. decision to put off sanctions on Iran for new violations in recent weeks of United Nations Security Council resolutions.

The candidates did not elaborate on why they believe Clinton, who left the State Department in 2013, is responsible for Pyongyang's latest provocation, and most did not say in detail how they would respond to the regime. Rubio, speaking in Iowa, said he would return North Korea to a list of state sponsors of terror, add sanctions against officials with significant overseas assets, bolster Asia-Pacific military alliances and invest in a "comprehensive missile defense system for the entire continental United States." 

White House press secretary Josh Earnest said that "the initial analysis that's been conducted of the events that were reported overnight is inconsistent with North Korean claims of a successful hydrogen bomb test." 

He also said that the Republican candidates' criticism is driven "because they're trying to win votes from conservative Republicans in a presidential primary. And that's the way our process works, and they're certainly entitled to do that. But we've heard a lot of campaign rhetoric, but not a lot of specific, tangible suggestions about what should be done differently." He said Obama "is focused on confronting this challenge by making our national security interests the top priority" and said there is "no doubting" the U.S.'s "rock-solid commitment" to protecting allies such as South Korea and Japan in the region.

Clinton condemned what she said was North Korea's attempt to "blackmail the world into easing the pressure on its rogue regime.'' She also urged China to be more assertive in using its influence on the regime and to cut illicit trade across its border with the country.

 "We can't give in to or in any way encourage this kind of bullying,'' she said in a statement. "Instead, we should increase pressure and send Pyongyang an unmistakable message that its nuclear brinksmanship won't succeed.''

 The two other Democratic contenders, Bernie Sanders and Martin O'Malley did not issue statements in reaction to North Korea's claims in the initial hours following the blast, which occurred Wednesday morning local time, Tuesday night in Washington, and triggered a magnitude 5.1 earthquake.

However, the regime has a history of exaggerating its capabilities and analysts expressed skepticism given that the yield and seismic wave were consistent with a hydrogen bomb tests.

Condemnation also came from South Korea and Russia. NATO called it a violation of UN Security Council resolutions. The Security Council is meeting Wednesday to consider additional penalties for North Korea, already laboring under a broad set of sanctions. 

—Sam Kim, Elizabeth Titus and Sangwon Yoon contributed to this report.

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