The ministers said they needed to know details of the US president-elect's plans but said they expected good ties.
The talks took place at a dinner in Brussels on Sunday, on the eve of a formal meeting of foreign ministers.
Ministers from Britain, France and Hungary did not attend on Sunday.
"We are looking forward to a very strong partnership with the next [US] administration," EU foreign policy chief Federica Mogherini said.
"We have decided together to engage with the incoming administration even from this very first week of transition," she added.
Belgian Foreign Minister Didier Reynders told reporters: "Whatever the US administration, it has long been known that Europe will have to step up its action on security and defence."
During the campaign, Mr Trump suggested that the US may not automatically come to the aid of a Nato ally under attack.
Monday's formal meeting, which is being attended by ministers from all 28 member states, is due to discuss relations with Turkey and defence co-operation with Nato.
Mr Trump's election win has exposed rifts in Europe with some officials distancing themselves from discussions on future relations.
UK Foreign Secretary Boris Johnson said on Friday that it was "time we snapped out of the general doom and gloom" over the US result, referring to negative comments as a "collective whinge-o-rama".
Hungarian Foreign Minister Peter Szijjarto said Sunday's meeting was "completely premature" and hit out at "frustrated and hysterical statements" made by other European leaders following the US election result.
The statement from the ministers contrasts sharply with comments by European Commission President Jean-Claude Juncker, who warned on Friday that Mr Trump's election risked upsetting EU ties with the US "fundamentally and structurally".