WASHINGTON — The Korean War Veterans Memorial on the National Mall is often considered one of the most striking of the war memorials, with the seven-foot-tall stainless steel statues of soldiers anticipating combat, and its dark gray granite wall etched with images of those who supported the troops.

While more than 36,000 Americans died in the combat mission in the Korean War, historians often call it the “forgotten war.” And now, with the Korean War Veterans Memorial Foundation struggling to set up a maintenance fund for the memorial, and to build a Wall of Remembrance, those looking for the necessary financing are feeling forgotten all over again — the only backing is coming from overseas.

“Our greatest support comes from corporate Korea,” said William E. Weber, the chairman of the foundation and a retired colonel in the United States Army who served in the Korean War. “American corporations — forget it.” He said no American corporate entities had committed to supporting the foundation’s efforts to meet its $5 million fund-raising goal.

Because of budget shortfalls, the National Park Service is facing an $11.5 billion backlog on maintenance projects — more than $852 million of that applies to the National Mall and Memorial Parks department — and often turns to nonprofit groups to help maintain the war memorials for the millions of people who visit them each year.