Worth noting here that the accent falls on the second half of the word: ver-TRAG. A similar sounding word, Vortrag (lecture), has the opposite emphasis: VOR-trag. This is just one of those things I've had to deal with starting a new life in Germany. And Germans do love their contracts.
I suppose "contract" would be more common, but "treaty" does also translate to Vertrag so perhaps it will be added if you reported it.
Not a native speaker, but I think the word for treaty is "Abkommen".