The trip would have been the latest in a series of high-level visits by Trump administration officials to Taiwan that have drawn the ire of Beijing.
But European diplomats and other people familiar with the matter said Luxembourg's foreign minister and top European Union officials had declined to meet with him during his planned European trip this week.
Mr Pompeo announced the change last Saturday, which scraps curbs on meetings with Taiwanese officials, in the waning days of Republican President Donald Trump's administration before Democrat Joe Biden assumes the presidency next Wednesday.
Besides Stoltenberg, he was also set to meet Belgium's deputy prime minister and foreign minister.
Pompeo's plans to leave his mark on ties between Taipei and Washington took a hit on Tuesday when the State Department announced the cancellation of a planned trip to Taiwan by Kelly Craft, the USA ambassador to the United Nations.
Asselborn described Trump as a "political pyromaniac who must be brought before a court" over last week's attack on the US Capitol by his supporters.
"We are fully committed to the completion of a smooth and orderly transition process to be finalized over the next 8 days", spokesperson Morgan Ortagus said in a statement, adding the agency was "pleased with the level of cooperation and professionalism that has been displayed".
During an interview with CCTV, Teng Jianqun, director of the Department for American Studies and a senior research fellow at China Institute of International Studies, said that Trump's administration is trying to limit the space for Biden to adjust the government's policies toward China, especially with respect to Taiwan, so that Biden can't escape this "trap". A representative of China's mission to the United Nations in NY urged Washington to stop "creating obstacles" for the relationship between China and the United States.
The US ambassador to the United Nations, Ms Kelly Craft, is due to arrive in Taiwan today for a three-day visit, which has also angered Beijing.
It's unclear why Pompeo wanted to make the quick trip to Brussels with less than a week in the administration.
"Shocking scenes in Washington, DC".
But Biden, who favors a far less confrontational diplomatic style that Trump, has given few details on what his Taiwan policy might be.
For the next U.S. administration, Nachman believes, the move could pose a challenge, by forcing the incoming secretary of state, Anthony Blinken, to address the issue of Taiwan in the first few weeks of the new administration.
"I regret very much that President Trump since November has not conceded his defeat - and not yesterday either".
On Monday, China's Foreign Ministry strongly condemned Pompeo's announcement.