English did not go into detail. But reforms which came after the rise of the Islamic State three years ago give the Government greater powers to monitor suspected terrorists or suspend their passports.
Taylor has previously said he wanted to remain in Syria, and he has burned his New Zealand passport. However, he is still able to apply for emergency travel documents.
English would not say what would happen if Taylor returned to New Zealand.
"That will be a matter of what risk he poses at the time and what his behaviour is."
He added: "We believe we've got sufficient powers to deal with any issues that arise, at the border if he's here. If he's in Syria, that's a big risk, I would have thought."
New Zealand's terror threat level remains at "low". It was raised from "very low" in 2014 in the wake of overseas attacks by foreign fighters associated with Isis.
There was no plan to raise the terror threat level, English said.
Taylor in the past has been called "the bumbling jihadist". He once mistakenly sent out his exact location in Syria by forgetting to turn off the tracking function on his phone.
The State Department is also declaring El Shafee Elsheikh as a global terrorist. He was one of the British-sounding captors accused of beheading hostages.
The US is also targeting radical British preacher Anjem Choudary, who has said he will continue recruiting for Isis after being sentenced to a British prison.
Others included are an accused Swedish al Qaeda member, a Malaysian and Indonesian for allegedly plotting Isis attacks, and citizens of Tobago accused of fighting for Isis in Syria.