During a Monday morning appearance on "America's Newsroom," Keane supported a claim by the Defense Intelligence Agency director, Lt. Gen. Robert Ashley Jr., who said that Iran is nearing an "inflection point."
"President Trump is really the first administration in 39 years to be on the strategic offensive with the Iranians," Keane said. Existing sanctions on oil and other industries have already put considerable strain on the plummeting Iranian economy, and Trump said on Saturday he planned to impose even more sanctions on the country's exports.
Six oil tankers have been attacked over the last month, while a sophisticated U.S. spy drone was shot down by Iranian forces last week. Director Ashley told Fox News that it's likely the Iranians' goal is to shift the "status quo."
Keane said on Monday that this campaign is crucial because Iran needs to "change their behavior in the region and also their behavior with their own people."
The Fox News senior strategic analyst added that Iran likely assumed that they could provoke a response from Trump and his administration by shooting down the spy drone.
"The Iranians believe that what will take place is that the United States will begin to walk up the ladder of escalation by responding to that with a kinetic attack and retaliation," he said.
Trump, however, resisted a response - calling off a strike 10 minutes before it was set to be launched after learning 150 people could die.
"Now he has leverage with the allies to give him some assistance. And secondly, he's increased the sanctions. So this thing has just really backfired in the Iranians' face," Keane added.
Because of the president's restraint, Secretary of State Mike Pompeo is in a better position to negotiate with allies to protect American interests in Iran, according to Keane.
"I also think it is worth a try to try to get them to assist in participating in the sanctions as well," he said. "I think there is potential here for some progress on the part of the Trump administration and our allies and partners."