The White House on Monday disputed claims by Senate Minority Whip Jon Kyl that President Barack Obama told him that he would not secure the U.S.-Mexico border until Congress advances comprehensive immigration reform.

During remarks at a tea party gathering in Arizona last week, the Arizona Republican said Obama told him in a private meeting that he would not prioritize border security until Congress moves on broader immigration reform legislation. “The problem is, he said, ‘If we secure the border, then you all won’t have any reason to support comprehensive immigration reform,'” Kyl said.

The GOP Senator went on to criticize the president’s approach to border security, saying the administration is “holding it hostage” to broader immigration reform opposed by Republicans. Kyl has joined fellow Arizona Republican Sen. John McCain in pushing for additional security at the U.S.-Mexico border, and last month Obama vowed to deploy an additional 1,200 National Guard troops.

White House spokesman Bill Burton said Monday that Kyl’s comments were untrue.

“The president didn’t say that,” he said. “Sen. Kyl knows that the president didn’t say that.” Asked whether Kyl lied or just exaggerated the details of his conversation with the president, Burton said, “I’ll let other folks make that determination.”

Burton said Kyl should expect that the White House “will be in contact with his office” over the matter. Kyl spokesman Ryan Patmintra said that his office has yet to hear from administration officials and that Kyl is fairly portraying their discussion.

“There were two people in that meeting, and neither Bill Burton nor [White House Communications Director] Dan Pfeiffer was one of them,” Patmintra said. “Sen. Kyl stands by his remarks.”