As President Obama focused intently on locking in a high-stakes nuclear deal with Iran, his administration pursued a decidedly less clear strategy on containing North Korea, a rogue state that already possesses an atomic weapon.

This week, Pyongyang rattled the United States and its Asian allies by claiming to have successfully tested a hydrogen bomb, an act that, if confirmed, would represent a major step for that nation’s nuclear arsenal. Even if the bomb turns out to be less powerful than advertised, the test alone highlighted a conundrum for a president who has made nuclear disarmament a cornerstone of his foreign policy agenda.

The White House quickly condemned the test as a “provocative and flagrant” violation of U.N. Security Council resolutions and promised to pursue punitive sanctions. But the unwillingness of North Korean dictator Kim Jong Un to respond to international pressure in a fashion similar to the government in Iran has left the Obama administration with few obvious options and opened the president to criticism Wednesday that he has been too cautious in his approach.

“North Korea is run by a lunatic who has been expanding his nuclear arsenal while President Obama has stood idly by,” Sen. Marco Rubio (Fla.), a Republican presidential candidate, said in a statement. “Our enemies around the world are taking advantage of Obama’s weakness.”

Aides said Obama spoke with the leaders of two U.S. allies, Japan and South Korea, and his national security adviser, Susan E. Rice, met with the Chinese ambassador in Washington.

After North Korea's claim that it tested a hydrogen bomb, The Post's Karen DeYoung explains why the U.S. response to the rogue nation is so different from how it treats Iran. (Jason Aldag,Gillian Brockell/The Washington Post)

But North Korea’s fourth nuclear test — its first since 2013 and the third during Obama’s presidency, and in a region where Obama has sought to intensify U.S. diplomatic and military attention — renewed concerns about the administration’s policy of “strategic patience” in dealing with Pyongyang.

“The fact that we see provocative acts from North Korea is an indication we are not getting the results we’d like to see yet,” White House press secretary Josh Earnest acknowledged at his daily briefing. “We’re concerned about the destabilizing impact North Korea’s provocative acts will have on the broader region.”

Earnest dismissed GOP criticism as overheated campaign-trail rhetoric aimed at conservative primary voters and countered that Republicans have offered no reasonable alternatives for dealing with Pyongyang. The Obama administration has maintained economic sanctions on North Korea and sought to strengthen ties with regional allies, bolstering U.S. military exercises and resources.

“It’s true that we have not achieved our goal,” Earnest said. “But we have succeeded in making North Korea more isolated than ever before and the international community more united than ever before.”

Republican leaders scoffed at that assessment and suggested that Pyongyang’s belligerence is part of a pattern of behavior from rogue states during the Obama presidency. House Speaker Paul D. Ryan (R-Wis.) cited Obama’s decision not to enforce a ­self-proclaimed “red line” after Syria used chemical weapons in 2013 and said the North Korean nuclear test “is exactly what happens when we appease and embolden rogue regimes.”

Ryan added that the situation on the Korean Peninsula, where the North violated a nuclear deal during Bill Clinton’s administration, should cast doubt on the sanctity of Obama’s Iran deal.

The difference between the level of U.S. engagement with Iran and with North Korea led some Asia analysts to conclude that the administration had downgraded the latter country as a national security priority.

Eight countries. 2,054 nuclear tests. 70 years – mapped

As Obama has pursued an Asia strategy that includes a 12-nation Pacific Rim trade accord, the diplomatic opening of Burma and a climate pact with Beijing, he has failed to spend as much political capital on pressing China to force North Korea to the negotiating table, said Victor Cha, who served as senior Asia director for the National Security Council in the George W. Bush administration.

“China does not seem to have been trying very hard on North Korea,” said Cha, now an analyst at the Center for Strategic and International Studies. “This is China’s responsibility, but the administration could have done more to make this a higher priority. When the president sits down with the Chinese president, there’s a list of things they want to talk about. My guess is North Korea is fifth or sixth on the list. During the Bush administration, it was the top issue on the list.”

Obama signaled early in his administration that he would elevate nuclear disarmament. When he accepted the Nobel Peace Prize in Norway in December 2009, Obama declared that preventing the spread of nuclear weapons was an “urgent” priority and added that it is “incumbent upon all of us to insist that nations like Iran and North Korea do not game the system.”

Yet White House officials said Wednesday that the president and his advisers viewed the two nations differently upon taking office. Unlike Iran, North Korea achieved nuclear weapons capability during the George W. Bush administration, Obama aides said, meaning that its incentives were different.

Kim, who assumed power in 2011 after the death of his father, has proved unresponsive to resuming the nuclear talks between North Korea, the United States, China, Japan, South Korea and Russia that began in 2003 but collapsed several years later with little progress.

Evan Medeiros, who served as senior Asia director in the Obama administration from 2013 to 2015, said the administration’s strategy was to “tighten the noose and to disrupt the old cycle of North Korea using a nuclear tantrum” to gain international attention to sue for sanctions relief.

On China, Medeiros added that after Xi Jinping assumed the presidency in 2013, the United States “made a huge play to say: ‘Okay, this is on you. If you care so much, you work on this and put some skin in the game. We’ve done a lot, and now we are focused on our allies Japan and South Korea and building up our military capability for deterrence and response.’ ”

In December 2014, the Obama administration pressed Beijing to help respond to alleged North Korean hacking after a highly publicized breach of Sony Pictures. A senior administration official who was not authorized to speak on the record said Wednesday that Beijing maintains leverage on Pyongyang “but they’re not prepared to use all of it.”

The official added: “What we have seen in the past from Republicans is either bluster or a call for a more muscular response, such as regime change or active military steps. It’s something we’ve considered, but we do not believe is stable or credible. We’ve also looked at the Bush administration’s record of engagement and talking and pressure and incentives. Neither of those were successful either. Nobody is asleep at the switch or resigned to the current situation.”