"I wish the US government (will) study our proposal properly and provide answers to the proposal," Ri Yong-Ho, the North's chief nuclear negotiator, told reporters after two days of unofficial talks with former US diplomats and security experts in Singapore.
Stephen Bosworth, the former special envoy for North Korea policy who led the US side, stressed that he and his colleagues met with the North Koreans as private citizens and did not come with any proposals from their government.
"We will have discussions when we get back but I would like to emphasise that we are not representing the US government or carrying any messages or proposals."
The United States earlier this month rejected the proposal, which had been passed to the US side through a "relevant channel", according to North Korea's official KCNA news agency.
US State Department spokeswoman Jen Psaki described the proposal as an "implicit threat" and accused the North of "inappropriately" linking routine military exercises between Washington and Seoul to the possibility of a nuclear test.
He said the North Koreans provided "detailed information of the intention and purpose" of their government's offer at the Singapore meeting.
"Part of the proposal is that if (the) United States puts a temporary halt to this large scale joint military exercise... We are ready to respond to the measures by putting a moratorium on the nuclear tests," Ri said through an interpreter.
The United States, which has close to 30,000 troops permanently stationed in South Korea, conducts a series of annual joint military exercises with its key Asian ally.
The annual exercises habitually raise military tensions between the two Koreas, who have remained technically at war since the 1950-53 Korean War concluded with a ceasefire rather than a peace treaty.
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