Sanders later told reporters that there are now no plans for a second summit.
The White House said Thursday that President Donald Trump had received a new letter from North Korean dictator Kim Jong Un, without disclosing its contents.
The repatriation of 55 boxes of US service members was part of the commitment made by Trump and Kim in their Singapore summit on June 12.
"Chairman Kim made a commitment to denuclearize", Pompeo told reporters.
North Korean Foreign Minister Ri Yong Ho is also in Singapore and will attend the same regional meeting as Pompeo on Saturday, but the State Department has not said whether the two will meet.
In July, Kim Jong Un's regime said the USA was making "gangster-like" demands following a meeting with Secretary of State Mike Pompeo. I am not at all surprised that you took this kind action.
With little public sign of progress toward Trump's aim of Korean denuclearization, the White House said the letter followed up on the pair's June 12 summit.
Pompeo said: "The world should be less nervous than the world before the summit between the two leaders, where we were in a very hard place with frequent missile launches and nuclear testing taking place".
Trump tweeted about the letter on Thursday, thanking Kim for returning the remains of some American war dead from the 1950-1953 Korean War.
Trump, top European leader agree to work toward zero tariffs
But Trump later reversed course and said the United States would impose a 25% tariff on $50 billion of Chinese exports. Since then, each side has imposed tariffs on $34 billion of the other's imports, and they've threatened to go further.
Military members stood at attention Wednesday at Joint Base Pearl Harbor-Hickam after placing transfer cases in a hangar at a ceremony marking the arrival of remains believed to be of American service members who fell in the Korean War.
While it is hoped that the repatriation will give momentum to the implementation of the key element of the deal - the dismantlement of North Korea's nuclear weapons program - progress toward securing firm commitments in that regard from Pyongyang has reportedly been slow.
Trump has maintained his optimism about North Korea's denuclearization, while saying there is no time limit on the negotiations.
Mr Pence said the handover demonstrated the success of President Trump's summit with Mr Kim.
"I think it's going to work out very well", he told supporters at a rally in Tampa, Florida, on Tuesday night. "A lot of good things are happening".
"No tests, no rockets flying. But we'll see what happens", Trump said.
On Monday, a senior US official said USA spy satellites had detected renewed activity at the North Korean factory that produced the country's first intercontinental ballistic missiles capable of reaching the United States.
The Washington Post, citing officials familiar with U.S. intelligence, reported this week that North Korea appears to be building up to two liquid-fueled intercontinental ballistic missiles.
When the North Koreans turned over the 55 boxes to Byrd and other USA officials at Wonsan on July 27, they said the cases contained remains of an undetermined number of Americans, but the only identification item provided was a single military dog tag, Byrd said.