Washington (CNN) The White House is continuing its push to temper expectations around a potential face-to-face meeting between President Donald Trump and North Korean leader Kim Jong Un -- insisting that the US will not negotiate any concessions until Pyongyang takes concrete steps toward dismantling its nuclear and missile programs.

Trump immediately touted North Korea's pledge over the weekend to suspend its nuclear and missile tests as a sign of "progress," but on Monday, White House press secretary Sarah Sanders emphasized that the US is "not naive in this process" and is "not going to make mistakes from previous administrations."

"We're not going to take the North Koreans at their word. The maximum pressure campaign is going to continue until" there are concrete steps toward denuclearization," she said. "We're not naïve in this process. We've seen some steps in the right direction but we have a long way to go."

Kim said on Friday that North Korea's quest for nuclear weapons is "complete" and it "no longer needs" to test its weapons capability -- a significant development ahead of diplomatic engagement with South Korea and the United States.

The announcement appeared to signify a remarkable change in policy for Kim following a relentless pursuit of nuclear and ballistic weapons as a means to ensure his regime's survival.

"North Korea has agreed to suspend all Nuclear Tests and close up a major test site," Trump tweeted. "This is very good news for North Korea and the World - big progress! Look forward to our Summit."

But Trump's tone shifted on Sunday as he responded to criticism that Pyongyang is getting more out of the talks than Washington -- declaring that the US has not "given up anything" in negotiations with North Korea.

"Wow, we haven't given up anything & they have agreed to denuclearization (so great for World), site closure, & no more testing!" Trump tweeted.

The President followed up with a second tweet that said, "We are a long way from conclusion on North Korea, maybe things will work out, and maybe they won't -- only time will tell."

Pressure campaign will continue

Asked on Monday whether Kim's announcement suspending nuclear tests and missile launches was a positive sign, Defense Secretary James Mattis said there are "reasons for optimism."

"Right now, I think there is a lot of reasons for optimism that the negotiations will be fruitful and we'll see," he said.

But while the US and South Korea welcomed the gesture -- which they said was a sign of progress and a promising start to upcoming talks -- the White House made it clear that the administration will negotiate with North Korea on its own terms.

"The goal is denuclearization of the peninsula and we're going to continue the maximum pressure campaign that has been ongoing to North Korea until we see concrete actions taken toward complete and total denuclearization," Sanders said.

Asked whether the US would continue a phased lifting of the sanctions as a reward for incremental progress, Sanders again said "no sanctions" will be lifted "until we see concrete actions taken by North Korea to denuclearize."

Notably absent from the White House's push to frame the terms of the potential summit between Trump and Kim has been any direct reference to the three Americans currently being detained by North Korea.

A US official said last week that Trump's Secretary of State nominee Mike Pompeo raised the issue of the detained Americans when he secretly met with Kim in Pyongyang to lay the groundwork for direct talks between Trump and Kim about North Korea's nuclear weapons program.

Trump himself said that the administration is "fighting very diligently" to get the US citizens back and that there is a "very good dialogue" -- but whether those talks are directly linked to negotiations over North Korea's nuclear program remains unclear.

Who has the upper hand?

North Korea continues to make concessions ahead of talks with South Korean President Moon Jae-in and the planned encounter between Kim and Trump which is expected to take place in late May or early June.

Last month Kim told a South Korean delegation he "understood" the need for joint US-South Korean military drills. Earlier this week he dropped his requirement that US troops leave the Korean Peninsula as a precondition for denuclearization.

A North Korea source told CNN that Kim has finally decided to open up a new chapter for his nation. Kim has committed himself to the path of denuclearization and will now focus solely on economic growth and improving the national economy, the source said.

The North Korean leader has realized the best path forward is to normalize relations with other countries, the source added. He is finally being recognized by the international community, and this is a historic, timely opportunity, the source said.

But while Kim's pledge to suspend nuclear and missile tests ahead of a potential meeting with Trump is almost universally viewed as a positive step, several analysts have warned against putting too much stock in the gesture.

"The announcement greatly increases the odds the summit with the United States occurs, which North Korea greatly values," according to Kingston Reif, the director for disarmament and threat reduction policy at the Arms Control Association.

"But it also seems that Kim Jong Un believes he is negotiating from a position of strength and is attempting to portray North Korea as legitimate and responsible nuclear power and seeking recognition as such," he said.

While "the cessation by North Korea of nuclear and ICBM testing and closure of its nuclear test site is significant and encouraging," Reif points out that Kim's announcement makes no mention of denuclearization and that "many risks remain, including that Trump's expectations, exacerbated by national security adviser John Bolton, are unrealistic."

"A successful summit would consist of actions by both sides to lock in these commitments -- which are reversible -- and start a sustained process to achieve further, verifiable constraints on North Korea's nuclear capability and reduce the risks of conflict," he told CNN.

Adam Mount, a senior fellow and the director of the Defense Posture Project at the Federation of American Scientists, told CNN that there is a whole range of deals that could meet American interests but "in none of them does Kim Jong Un hand over his nuclear arsenal for nothing but an IOU."

"Kim Jong Un's speech was a statement of his nation's nuclear weapons policy. In some ways, it was the opposite of a promise to denuclearize," he said. "Pyongyang is essentially trying to play for time. They will be looking for ways to distract attention from nuclear disarmament or to stall out negotiations."

"There is no realistic chance that North Korea will be nuclear-free by Christmas," Mount added. "The first step in negotiations must be to expand Kim's voluntary limits into a hard cap on his advancement so that negotiators have time to work toward a comprehensive deal."