The law doesn't make exceptions for foreign nationals that the US has a treaty with.
The take care clause doesn't require that the president pursue any particular crime or every single crime.
"To be sure, the extent of the faithful-execution duty is rather unclear. Plainly, the President need not enforce every law to its fullest extent. Common sense suggests that the President may enjoy some discretion in order to gauge the costs and benefits of investigation, apprehension, and prosecution."
^ and that's from the Heritage Foundation
By virtue of his executive power, the president may execute federal laws and control officers who execute those laws.
www.heritage.org