"This summit was a crucial and necessary step to build upon the positive developments achieved in inter-Korean relations and on the peninsula so far," the EU's diplomatic chief Federica Mogherini said in a statement.
Mogherini stressed that the aim of the international community remained "the complete, verifiable and irreversible denuclearisation of the Korean Peninsula" -- a longstanding formulation that implies Pyongyang allowing inspections and not rebuilding any weapons it gives up.
"The joint statement signed by the US and DPRK leaders today gives a clear signal that this goal can be achieved," Mogherini said, using an abbreviation for the North's official name, the Democratic People's Republic of Korea.
But Trump and Kim's joint statement omits the words "verifiable and irreversible", leading some observers to question whether it amounted to any new commitments from Pyongyang.
The US leader said there would be further meetings and Mogherini said the EU stood ready to "facilitate and support the follow-on negotiations and other steps".
Tensions between the EU and US are running high over a series of disagreements on major international issues, including Trump's withdrawal from the Iran nuclear deal and his decision to slap tariffs on steel and aluminium imports.