He also reiterated his belief in his good relationship with North Korean leader Kim Jong-un despite the collapse last week of their second summit.
"I would be surprised in a negative way if he did anything that was not per our understanding. But we'll see what happens," Trump told reporters. "I would be very disappointed if I saw testing."
Trump's comments came after two U.S. think tanks and Seoul's spy agency said this week that North Korea was rebuilding a rocket launch site at Sohae in the west of the country.
There have also been reports from South Korea's intelligence service of new activity at a factory at Sanumdong near Pyongyang that produced North Korea's first intercontinental ballistic missiles capable of reaching the United States.
On Friday, U.S. National Public Radio quoted experts from California's Middlebury Institute of International Studies as saying that satellite images of Sanumdong taken on Feb. 22 and on Friday suggested North Korea could be preparing to launch a missile or a space rocket.
One of the experts, Jeffrey Lewis, told Reuters the activity at the two sites was "probably connected." NPR said the Feb. 22 photos showed cars, trucks, rail cars and two cranes at Sanumdong, while in those taken on Friday, the activity had died down and one of the cranes had disappeared.
Other experts, including Joel Wit at 38 North and Michael Elleman of the International Institute for Strategic Studies considered the conclusion speculative.
"In the past there have been multiple reports about activity at this place that turned out to be false alarms," Wit said, referring to Sanumdong. "It could either be preparation for an eventual launch or not."
The White House and the Pentagon did not immediately respond to requests for comment. The State Department declined to comment.
North Korea has frozen nuclear and missile testing since 2017, and Trump has pointed to this as a positive outcome from nearly a year of high-level engagement with North Korea.
Sohae has been used in the past to test missile engines and to launch rockets that U.S. officials say have helped development of North Korea's weapons programs. A senior U.S. State Department official said on Thursday that any launch from there would be "inconsistent" with North Korean commitments.
Kim pledged at a first summit with Trump in Singapore in June that the engine test site and launch platform at Sohae would be dismantled. He repeated the pledge in a summit with the South Korean president in September.
Trump said he thought his and the U.S. relationship with Kim and North Korea was "a very good one."
"I think it remains good," he said.
Summit collapse
Trump has been eager for a big foreign policy win on North Korea which has eluded his predecessors for decades and has repeatedly stressed his good relationship with Kim.
He went as far late last year as saying that they "fell in love," but the bonhomie has failed to bridge the wide gap between the two sides and a second summit between them collapsed last week in Vietnam over differences on U.S. demands for Kim to give up his nuclear weapons and North Korea's demands for sanctions relief.
U.S. National Security Adviser John Bolton and other U.S. officials have sought to play down the developments spotted at Sohae, although Trump on Thursday called recent North Korean activity "disappointing."
The senior State Department official who briefed reporters in Washington on Thursday said he would "not necessarily share the conclusion" of the think tanks that the Sohae site was operational again, but said any use of it would be seen as "backsliding" on commitments to Trump.
Pyongyang has used Sohae to launch satellites into space since 2011, and one such launch in April 2012 killed off an Obama administration deal for a freeze in North Korean nuclear and missile testing in return for food aid.
North Korean state media acknowledged the fruitless Hanoi summit for the first time on Friday, saying people were blaming the United States for the lack of an agreement.
"The public at home and abroad that had hoped for success and good results from the second ... summit in Hanoi are feeling regretful, blaming the U.S. for the summit that ended without an agreement," its Rodong Sinmun newspaper said.
The paper directed fiery rhetoric against Japan, accusing it of being "desperate to interrupt" relations between Pyongyang and Washington and "applauding" the breakdown of the summit.
Washington has said it is open to more talks with North Korea, but it has rejected an incremental approach to negotiations sought by Pyongyang and it remains unclear when the two sides might meet again.
U.S. Secretary of State Mike Pompeo said on Monday he was hopeful he would send a delegation to North Korea for more talks in the next couple of weeks, but had received "no commitment yet."
The senior State Department official who briefed reporters on Thursday declined to say whether there had been direct contact between the sides since the summit. He said Washington was keen to resume talks as soon as possible, but North Korea's negotiators needed to be given more latitude.
"There will necessarily need to be a period of reflection here. Both sides are going to have to digest the outcome to the summit," said the official, who spoke on condition of anonymity.
"Fundamentally, where we really need to see the progress, and we need to see it soon, is on meaningful and verifiable steps on denuclearization. That's our goal and that's how we see these negotiations picking up momentum."
The official said complete denuclearization was the condition for North Korea's integration into the global economy, a transformed relationship with the United States and a permanent peace regime on the Korean peninsula.
Bolton, who has argued for a tough approach to North Korea, said this week that Trump was open to more talks, but also warned of tougher sanctions if North Korea did not denuclearize.