After the emergence of the Islamic State group, the USA chose the Kurdish fighters to partner with on the ground.
Zarif said it is "futile to seek" USA permission, and questioned relying on security promised by the US, in a possible reference to both Turkey and the Kurds.
US-backed Kurdish fighters in the Syrian Democratic Forces (SDF) have been at the forefront of the fight against the Islamic State (IS) group in the war-torn country.
The officials, who were not authorized to discuss details of military intelligence, said there are between 5,000 and 10,000 Turkish troops along the border apparently ready to go. "We will not hesitate for a moment in defending our people", it said in a statement.
In a written statement Monday, Pentagon chief spokesman Jonathan Hoffman said the US does not endorse a Turkish military operation in Syria and will not support it. Hoffman says the Pentagon will work with allies and coalition partner nations to reiterate to Turkey that its potential military operation in Syria would have "possible destabilizing consequences" for Turkey and for the region. The U.S. then partnered with the Kurdish fighters to fight the Islamic State group, at the cost of thousands of fighters' lives.
Trump threatened Turkey with economic collapse Monday should Ankara take action in Syria he deems "off limits", ahead of a planned operation in the country's northeast.
Dozens of military vehicles were sent to the area following a U.S. troop withdrawal from north-eastern Syria.
"The Department of Defense made clear to Turkey-as did the President-that we do not endorse a Turkish operation in Northern Syria".
Turkey, which considers Kurdish fighters in Syria terrorists and links them to a decades-old insurgency in Turkey, has already launched two major incursions into northern Syria over the past years.
US officials told The Associated Press that Turkish troops on Tuesday were massed along the border in apparent preparation for an incursion across the border.
The Pentagon, meanwhile, says it is still trying to talk Turkey out of invading northeastern Syria.
Iran, Turkey and Russian Federation have been working together as part of the so-called Astana group on the Syrian war, talks that have run parallel to United Nations efforts to find a solution to the conflict.