"I call for the immediate placement of North Korea on the designated list of state sponsors of terror while lawmakers and President Trump work towards a solution with China and other allies", Garrett said.
North Korea was a top issue at the talks.
The President and his top aides have repeatedly highlighted that any progress in dealing with the hermit kingdom's burgeoning nuclear program would rely on China's involvement.
"While I greatly appreciate the efforts of President Xi & China to help with North Korea, it has not worked out", Trump wrote on Twitter.
"I would have that first because if people are that stupid that they still want to go to that country then at least they assume the responsibility for their welfare", McCain said.
His comments came amid outrage over the death of American student Otto Warmbier who was released from North Korea last week, but in a state of coma.
Geng said China has played a "positive constructive" role regarding North Korea because it is a responsible member of the worldwide community, and "not because of any pressure from other countries".
Mattis says China shares the US desire for denuclearization of the Korean Peninsula, and "continues to work this issue".
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The U.S. and China began high-level security talks Wednesday focused largely on North Korea, amid outrage in Washington over the death of an American college student after his imprisonment in the North.
Mr Warmbier was imprisoned in a North Korean jail last year, eventually sentenced to 15 years of hard labour for allegedly attempting to steal a North Korean propaganda banner. "There is no way that we can look at a situation like this with any kind of understanding", he added. "We also affirmed our strong commitment to cooperate, including through the United Nations, to realize our shared goal of denuclearization of the Korean Peninsula", he said.
U.S. President Donald Trump said on Tuesday he had spoken with Warmbier's family and praised them as "incredible".
"I have great confidence that China will properly deal with North Korea".
Tillerson said Trump would make a state visit to China this year, and Mattis said both sides agreed to expand military-to-military ties, signalling the new administration's determination to continue efforts to improve relations between the world's two largest economies, despite frustration over North Korea.
Like past presidents, Trump is finding the USA has limited scope for punishing North Korea, particularly over the arrest of US citizens.
U.S. Secretary of State Rex Tillerson repeated demands that North Korea release three other U.S. citizens it holds in detention: missionary Kim Dong Chul and academics Tony Kim and Kim Hak Song.
Tillerson's visit to Beijing in March was followed by Chinese President Xi Jinping's visit to the United States three weeks later.
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