U.S. President Donald Trump on Thursday said he had a "very productive" time with Democratic People's Republic of Korea (DPRK) leader Kim Jong Un, but he decided not to sign anything at this time.

Trump made the remarks during a press conference after his second summit with Kim in Vietnam's capital Hanoi.

He also said the DPRK wants sanctions lifted but the U.S. is not willing to do so.

Trump suggested that the U.S. side is not satisfied with the areas the DPRK promised to work on and demanded a bigger compromise from the latter on denuclearization.

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He said there were papers ready to be signed, but said he preferred to do it right rather to do it fast. 

He also expressed a willingness to maintain contact with the DPRK, and said Kim promised him that there would be no more rocket or nuclear tests.

During the press conference, the American president also commended China's role in facilitating the denuclearization of the Korean Peninsula, saying it has been "a big help". 

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Trump says China 'a big help' in addressing Korean Peninsula issues

However, Trump refused to say whether sanctions will be increased to put more pressure on the DPRK. 

The American president is expected to head back to the U.S. right after the press conference, which came after the second summit with Kim wrapped up earlier than scheduled.