Biegun was quoted as saying on Friday that the United States "has no intention of easing our unilateral or United Nations sanctions" against North Korea.
"However, within the context of the engagement that we have with the DPRK (North Korea), we are prepared to explore number of other things that could build trust," he said in contradictory remarks.
Biegun linked trust-building steps to the dismantling of North Korea’s nuclear weapons. "We do have a number of initiatives we'd like to look at as we begin the process of denuclearization in North Korea."
However, North Korea said on Thursday it will never unilaterally give up its nuclear weapons unless the US first removes what Pyongyang called a nuclear threat, Presstv Reported.
The statement carried by the official Korean Central News Agency suggested that North Korea will eventually demand the US withdraw or significantly reduce the 28,500 American troops stationed in South Korea.
On Thursday, US Secretary of State Mike Pompeo expressed hope for a second summit between President Donald Trump and North Korean leader Kim Jung-un.
The second summit has been scheduled for early next year, but it is unclear whether North Korea would agree to holding the summit.
The first meeting took place in Singapore in June, when dialog was opened up between the two countries on denuclearization of the Korean Peninsula after months of exchanging military threats.
Since then progress has stalled, with both sides accusing the other of dragging their feet and acting in bad faith.
Trump has repeatedly said that as long as the pressure is on and the crippling sanctions are in place he is “in no hurry” to reach a denuclearization deal with North Korea.
Washington seeks the complete and irreversible dismantling of North Korea’s nuclear weapons.
In Thursday’s statement, North Korea made clear it is sticking to its traditional stance on denuclearization. It accused Washington of twisting what had been agreed on in Singapore and driving post-summit talks into an impasse.
“The United States must now recognize the accurate meaning of the denuclearization of the Korean peninsula, and especially, must study geography,” the statement said.
“When we talk about the Korean peninsula, it includes the territory of our republic and also the entire region of [South Korea] where the United States has placed its invasive force, including nuclear weapons.
"When we talk about the denuclearization of the Korean peninsula, it means the removal of all sources of nuclear threat, not only from the South and North but also from areas neighboring the Korean peninsula,” the statement said.
On Sunday, North Korea hit out at the US for stepping up sanctions, warning that it could force a return to “exchanges of fire” and block the path to nuclear disarmament forever.
The North Korean Foreign Ministry issued a statement, saying the US policy of “maximum pressure” would be its “greatest miscalculation”.
It came after Washington slapped sanctions on three North Korean officials last week, including Choe Ryong-hae, a top aide to leader Kim Jong-un, for alleged human rights abuses.
Pyongyang said Washington had imposed sanctions up to eight times against companies, individuals and ships of North Korea, China and Russia and other third countries.
The US, the ministry said, is “bent on bringing ... relations back to the status of last year which was marked by exchanges of fire.”
The sanctions, it said, "will block the path to denuclearization on the Korean peninsula forever – a result desired by no-one.”