SEOUL, South Korea — South Korean officials on Monday indicated that President Trump and North Korea’s leader, Kim Jong-un, could agree on a joint political statement declaring an end to the 1950-53 Korean War when they meet in Hanoi, Vietnam, this week.

“The possibility is open,” said Kim Eui-kyeom, a spokesman for South Korea’s president, Moon Jae-in, referring to the results expected from the Trump-Kim summit meeting scheduled for Wednesday and Thursday. “We still don’t know exactly what format the end-of-war declaration will take, but there is an ample possibility of North Korea and the United States agreeing to such a declaration.”

Mr. Moon has strongly advocated an end-of-war declaration to build trust between North Korea and the United States and to prod the North to move toward giving up its nuclear weapons. The North and the United States have remained technically at war since the Korean War was halted in a truce in 1953, and Washington still keeps 28,500 troops in South Korea to prevent it from rekindling.

Until now, South Korean officials, who are closely monitoring pre-summit meeting negotiations between North Korea and the United States, had sounded skeptical that Mr. Trump and Mr. Kim would agree to an end-of-war declaration during their Hanoi meeting. The remarks by the South Korean spokesman indicated such a declaration was now being seriously discussed as Mr. Trump seeks to encourage Mr. Kim to take steps toward denuclearization.