U.S. Secretary Tillerson and Defense Secretary Mattis meet with Chinese State Councilor Yang Jiechi and Gen. Fang Fenghui, prior to the U.S.-China Diplomatic and Security Dialogue, at the State Department in Washington Thomson Reuters By David Brunnstrom

WASHINGTON (Reuters) - Top diplomats and defense chiefs from the United States and China began a day of talks in Washington on Wednesday looking for ways to press North Korea to give up its nuclear and missile programs.

The talks come a day after U.S. President Donald Trump said Chinese efforts to persuade North Korea to rein in its weapons programs had failed, ratcheting up the rhetoric after the death of an American student who had been detained by Pyongyang.

Trump's statement is likely to increase pressure on Beijing at the Diplomatic and Security Dialogue, which pairs U.S. Secretary of State Rex Tillerson and Defense Secretary Jim Mattis with China's top diplomat, State Councilor Yang Jiechi, and General Fang Fenghui, chief of joint staff of the People's Liberation Army.

The State Department says Wednesday's talks would focus on ways to increase pressure on North Korea, but also cover such areas as counter-terrorism and territorial rivalries in the South China Sea.

The U.S. side is expected to press China to cooperate on a further toughening of international sanctions on North Korea. The United States and its allies would like to see an oil embargo and bans on the North Korean airline and guest workers among other moves, steps diplomats say have been resisted by China and Russia.

Trump has had high hopes for greater cooperation from China to exert influence over North Korea, leaning heavily on Chinese President Xi Jinping for his assistance. The two leaders had a high-profile summit in Florida in April and Trump has frequently praised Xi while resisting criticizing Chinese trade practices.

"While I greatly appreciate the efforts of President Xi & China to help with North Korea, it has not worked out. At least I know China tried!" Trump wrote on Twitter.

It was unclear whether his remark represented a significant shift in his thinking in the U.S. effort to stop North Korea's nuclear program and its test-launching of missiles or a hardening in U.S. policy toward China.

China's Foreign Ministry said on Wednesday that Beijing had made "unremitting efforts" to resolve tensions on the Korean peninsula.

On Tuesday, a U.S. official said U.S. spy satellites had detected movements recently at North Korea's nuclear test site near a tunnel entrance, but it was unclear if Pyongyang was preparing for a new nuclear test, perhaps to coincide with Wednesday's high-level talks.

A South Korean Defense Ministry official said North Korea remained prepared to conduct a sixth nuclear test at any time but there were "no new unusual indications that can be shared.”

North Korea last tested a nuclear bomb in September, but it has conducted repeated missile tests since and vowed to develop a nuclear-tipped missile capable of hitting the U.S. mainland, putting it at the forefront of Trump's security worries.

(Additional reporting by Steve Holland in Washington and Michael Martina in Beijing; Editing by Jeffrey Benkoe)