WASHINGTON — President Trump and Secretary of State Rex W. Tillerson are once again at odds over how to deal with nuclear-armed North Korea after Mr. Tillerson declared on Tuesday that the United States was ready to open talks with the North “without precondition.”

The secretary’s comments were remarkably conciliatory for an administration that has repeatedly threatened North Korea with military action, and ruled out any negotiations, if it did not curb its missile and nuclear programs. But a few hours later, the White House distanced itself from his overture.

In an unusual statement released to reporters on Tuesday evening, the press secretary, Sarah Huckabee Sanders, said Mr. Trump’s position on North Korea had not changed — namely, that talks were pointless if the North’s leader, Kim Jong-un, continued to menace his neighbors.

“North Korea is acting in an unsafe way not only toward Japan, China, and South Korea, but the entire world,” she said. “North Korea’s actions are not good for anyone and certainly not good for North Korea.”