Trump remained polite and friendly throughout a news conference following his meeting with Burnham, offering largely diplomatic answers to potential flashpoint topics.
Speaking at the UN General Assembly on Tuesday, Trump asked whether he should "annihilate the Islamic Republic" or offer it a deal to rebuild before telling reporters that US and Iranian officials had met on the sidelines. Most of Iran's delegation walked out during his speech.
The agreement will enable the US to expand its military presence on Greenland through the modernisation and enlargement of its current Pituffik Space Base and the establishment of new defence areas at Narsarsuaq and Mestersvig.