Pompeo pressed Southeast Asian nations to maintain sanctions on North Korea but said he was optimistic that the deal to end the North's nuclear programme would be implemented.
Kyaw Soe Oo, 28, and his Reuters colleague, Wa Lone, 32, are facing up to 14 years in prison in Myanmar for allegedly violating the country's colonial-era Official Secrets Act.
It was important to maintain diplomatic and economic pressure, Pompeo said, adding the United States took very seriously any relaxation of UN sanctions against North Korea.
The United States said earlier this week it would invest US$113 million in technology, energy and infrastructure initiatives in emerging Asia.
Mike Pompeo admits there was still "a ways to go" on North Korea as Washington seeks to push Pyongyang to move faster along the path towards denuclearisation.
He will discuss common security and economic interests.
"Make no mistake. We will be watching what the IMF does,"
Pompeo said Washington wants a "free and open" Asia not dominated by any one country, an apparent reference to China's growing economic clout.
Some US sanctions on Iran are due to kick in next month, while more serious penalties targeting countries with companies importing Iranian oil take effect in November.
Speaking at a cabinet meeting chaired by US President Donald Trump, Pompeo, who held inconclusive talks in North Korea earlier this month, said progress had been made on some issues.
Nicholson, who leads the NATO-led Resolute Support mission, said the United States recognized it had a key role to play.
At NATO, Pompeo would discuss Iran with ministers from Britain, France and Germany, and in other bilateral meetings.
Pompeo said the peace process would be Afghan-led but added that the United States would be prepared to participate to help resolve differences and said support from neighbouring countries would also be needed.
U.S. Secretary of State Mike Pompeo raised the issue of a detained American man of Vietnamese descent during meetings with senior Vietnamese officials in Hanoi.
That North Korean assessment contradicted comments made on Saturday by Pompeo, who said he had made progress on "almost all of the central issues."
North Korea’s nuclear weapons, China’s military muscle-flexing in the region and closer US-Vietnam relations were expected to be the main discussions between Pompeo and Vietnamese leaders.
The North's foreign ministry said the "extremely regrettable" US attitude during the meeting violated the spirit of the agreement reached between leader Kim Jong Un and President Donald Trump at their Singapore summit.
Pompeo said that North Korea, in the “many hours of talks’’ at a walled-off guesthouse outside downtown Pyongyang, reiterated its commitment to denuclearization.
Pompeo held two days of meetings with senior North Korean officials led by top Kim aide, Kim Yong Chol, on concerns ranging from the regime’s nuclear arsenal to US security guarantees.
The State Department on Thursday denied that the United States had softened its approach toward North Korean denuclearization, as US Secretary of State Mike Pompeo heads to Pyongyang hoping to hammer out a roadmap for its nuclear disarmament.
Washington's top diplomat and senior aides took off shortly after 2.00am and were due in the North Korean capital on Friday, where Pompeo is to stay overnight for the first time.
The United States appears to have shelved an "all or nothing" approach to North Korean denuclearization as US Secretary of State Mike Pompeo prepares to head back to North Korea this week.
The moves illustrate how far Kim remains from surrendering his nuclear weapons despite committing to “work toward complete denuclearization of the Korean Peninsula” during his meeting with Trump.
His visit would mark the first to North Korea since US President Donald Trump and North Korean leader Kim Jong Un held their June 12 summit in Singapore.