Trump is due in Brussels next week to meet EU and NATO leaders on his first foreign trip since taking office in January.
Trump is due in Brussels next week to meet EU and NATO leaders on his first foreign trip since taking office in January on a promise to force allies to take on more of the defence burden.
"I very much appreciate the cooperation we have inside NATO on information sharing," Stoltenberg told reporters when asked about Trump's conduct.
"I trust all allies enough and I am absolutely certain that they are able to share and to handle this information in a good way," he said as he went into a meeting with EU defence ministers on increasing security cooperation.
Stoltenberg noted that NATO's 28 member countries, led by the United States, have been exchanging sensitive information for years, and in 2016 the alliance created a top intelligence coordination unit to improve such exchanges.
Trump, who has been sharply critical of the EU and even described NATO as "obsolete" at one point, caused dismay after reports he disclosed intelligence about a possible Islamic State terror threat during a meeting with Russian Foreign Minister Sergei Lavrov last week in Washington.
It subsequently emerged that staunch US ally Israel may have been the source of the information, adding fuel to the fire.
Established diplomatic norms mean that intelligence is rarely discussed in public, that it is shared only very carefully with allies, and that its source is rarely if ever disclosed.
Trump's problems, and the turmoil over his administration's possible Russian links, have raised eyebrows in Europe but political leaders and officials have been reluctant to discuss the matters publicly.