SEOUL, South Korea — With the United States and North Korea locked in an escalating exchange of threats, South Korea told its people on Friday that the White House had agreed not to do anything on the Korean Peninsula that would catch the South off guard.

Chung Eui-yong, the top national security adviser for President Moon Jae-in of South Korea, talked on the phone with his American counterpart, Gen. H. R. McMaster, on Friday morning. The 40-minute conversation came as jitters among South Koreans were growing over President Trump’s threat to deal with North Korea with “fire and fury” and the North’s warning that it would respond with an “enveloping” missile barrage around Guam, home to major American military bases.

“Both South Korea and the United States reaffirmed their promise that as they take step-by-step measures to ensure their security and the safety of their peoples, they will coordinate with each other closely and transparently,” the presidential spokesman Park Soo-hyun said in a statement after Mr. Chung’s talk with General McMaster.