Peters is also understood to have welcomed Trump's decision last week to rescind the policy of separating children at the southern border from non-documented arrivals.
The pair are expected to meet at a regional forum in Asia in August.
Pompeo visited New Zealand in April last year for an intelligence conference in Queenstown in his former capacity as director of the Central Intelligence Agency.
Before taking up that job he was a Republican member of the House of Representatives, representing Kansas.
Pompeo was instrumental in setting up the summit between Trump and North Korean leader Kim Jong-un.
New Zealand manufactures steel at Glenbrook, south of Auckland, and aluminium at Tiwai near Invercargill.
According to Trade Minister David Parker, iron and steel exports to the US last year were worth $39 million out of a global total of $433m, and aluminium exports to the US were worth $23m out of a total of $1.1 billion.