At the same time, other Twitter users have expressed their discontent with the prospect of Trump and Kim Jong-un getting the Nobel Peace Prize. The Nobel Committee in Oslo typically receives hundreds of nominations each year, and past candidates have also included Russian President Vladimir Putin and Former Cuban leader Fidel Castro.
Nominations for this year's prize also formally closed on February 1, before the summit was agreed.
Trump was nominated by two right-wing members of Norway's Progress Party, which advocates for limited immigration and lower taxes.
The lawmakers told Norwegian wire service Norwegian News Agency that Trump "had taken a huge and important step" toward peace with North Korea and disarmament.
Trump's potential nomination makes him eligible for the 2019 Nobel Peace Prize, as the 2018 process ended last January.
The North Korean situation has been rocky as it has unfolded, but there has been significant progress.
During the summit, Trump and Kim signed a brief document committing the U.S.to unspecified security guarantees for North Korea in exchange for the denuclearization of the Korean Peninsula.
2017 prize went to the International Campaign to Abolish Nuclear Weapons (ICAN).
Former recipients have included Martin Luther King Jr., Mother Teresa, Malala Yousafzai, Nelson Mandela, and Trump's predecessor, Barack Obama. North Korea also agreed to return the remains of American military personnel killed in that country during the Korean War from 1950 to 1953.
Five Labour frontbenchers quit over Brexit vote
It also seeks to hand the negotiations over to parliament after February 15 2019 if a deal has not been agreed by that time. That has potentially seismic consequences for the protracted and increasingly messy split from Brussels.
US Federal Reserve raises interest rates
Economists are predicting unemployment will drop slightly to 5.5 per cent, with 18,000 new jobs created. Unemployment is 3.8%, the lowest since 2000, and inflation is creeping higher.
Will North Korea agree to complete denuclearisation?
President Donald Trump nears, Kim has reason to be nervous. "I could see Trump giving up a lot for very little in return". The two clasped hands for a long while Tuesday as they posed for photos in front of a row of USA and North Korean flags.