North Korea also called off high-level talks with South Korea scheduled for Wednesday, blaming U.S.
While speaking to reporters following the return of three American hostages from North Korea last week, Trump said, "My proudest achievement will be - this is part of it - when we denuclearize that entire peninsula".
"We're going to continue with the campaign of maximum pressure if that's the case", Sanders said.
Trump's new national security adviser, John Bolton, known for his hard-line stance against North Korea, is pushing for Libya's model, asserting that North Korea should unilaterally abandon all its nuclear weapons.
Donald Trump's upcoming summit with North Korean dictator Kim Jong Un has been treated as a victory for the president's bellicose approach to foreign policy.
The spokesperson also reiterated the Chinese proposal of a freeze-for-freeze or "double suspension" deal between the USA and the DPRK, which would see North Korea halt missile and nuclear tests in return for the US suspending joint military drills with South Korea.
Bolton must have known the Libya comparison carried dark connotations for North Korea, but he said it anyway, despite the fact that North Korea and Libya have extremely different weapons programs and geopolitical situations. We'll see what happens.
"The president is very used to and ready for tough negotiations", she continued.
The North Korean warning follows a weeks-long charm offensive that has seen Kim Jong-un hold a historic summit with the South's president and meet twice with Chinese President Xi Jinping.
If it does go ahead, it will be the first ever face-to-face meeting between a North Korean leader and a US President.
In an angrily worded statement, the North warned on Wednesday it may back out of the high-level summit if the United States pressures it to give up its nuclear arsenal. "North summit [without trying to get anything else first] so I think Pyongyang is briefly trying to put the brakes on [the current situation] ahead of the summit".
"The DPRK (Democratic People's Republic of Korea) side emphasised that, as a friendly country, DPRK will never allow any action that would create concerns for India's security", the External Affairs Ministry statement said.
He also criticised other United States comments that the North should completely abandon not only its nuclear weapons and missiles but also its biological and chemical weapons. It began on Monday and is slated to run through May 25, and is expected to include aircraft from the U.S. Air Force, Army, Navy and Marine Corps, as it has in the past. The North Korean news agency KCNA said the Max Thunder exercises are a "rehearsal for invasion" of North Korea and a provocation.
While the glaring gap between America and North Korea about what constitutes denuclearisation may be expected at this stage of the process, there is a worrying lack of clarity from the USA about what it wants from the Singapore summit.
The Trump administration has insisted on complete, verifiable, and irreversible dismantling of North Korea's nuclear weapons and the facilities needed to build the weapons as soon as possible. -South Korea military drills in cancelling the meeting with officials from Seoul.
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