By Doina Chiacu and Susan Heavey
WASHINGTON (Reuters) - Republican U.S. presidential candidates on Wednesday blamed President Barack Obama's "feckless" and "failed" foreign policy for allowing North Korea to build its nuclear arms capabilities, with front-runner Donald Trump urging China to rein in its ally or face trade repercussions.
North Korea said it tested a miniaturized hydrogen nuclear device on Wednesday on orders from leader Kim Jong Un. Some analysts questioned whether it was indeed a test of a full-fledged hydrogen device.
Trump, leading the race for the Republican nomination in November's election, said the United States was not doing enough to make China more accountable for North Korea's actions.
"Nobody is talking to them whatsoever, and nobody is discussing it with China. China has total control, believe me. They say they don't - they have total control over North Korea, and China should solve that problem," Trump said on Fox News.
"And if they don't solve the problem, we should make trade very difficult for China. ... North Korea is totally under their control. Without China, they wouldn't eat," added Trump, who called Kim a madman.
Republican presidential candidates routinely call Obama's foreign policy weak. They have criticized the agreement to contain Iran's nuclear program and the U.S. response to Middle East crises including Syria's civil war and Islamic State's rise.
"If this test is confirmed, it will be just the latest example of the failed Obama-Clinton foreign policy," Senator Marco Rubio said in a statement late on Tuesday. Rubio was referring to Obama's former secretary of state Hillary Clinton, front-runner for the Democratic presidential nomination.
"I have been warning throughout this campaign that North Korea is run by a lunatic who has been expanding his nuclear arsenal while President Obama has stood idly by," Rubio said.
Jeb Bush, whose brother George W. Bush was president when North Korea conducted its first nuclear test in 2006, said on Twitter: "North Korean nuke test shows danger of continuing feckless Obama/Clinton foreign policy." North Korea has carried out three nuclear tests since.
Texas Senator Ted Cruz, a close challenger to Trump, told a radio interviewer the United States needs a commander in chief with the knowledge, judgment and resolve to keep the country safe.
Obama has failed to keep North Korea in check, Governors Chris Christie of New Jersey and John Kasich of Ohio said.
"The Obama administration has been asleep at the switch on North Korea, and that inaction has allowed serious and destabilizing actions like this to occur," Kasich said in a statement.
Kentucky Senator Rand Paul advocated drawing on China's influence with North Korea and possibly increasing sanctions on the isolated communist state.
"There are no easy solutions," Paul told CNN. "You want me to magically wave a wand and all of a sudden their nuclear weapons are gone?"
Clinton has not weighed in. Her closest Democratic challenger, Vermont Senator Bernie Sanders, said the first U.S. step should be to "lean on" China to push North Korea to start adhering to international agreements.
(Additional reporting by Steven Holland, Susan Heavey and Alana Wise; Writing by Doina Chiacu; Editing by Will Dunham)