In a communication to the Congress today, Trump also sought USD 1.2 billion to support sending additional 3,500 troops to Afghanistan as part of his new South Asia strategy and a further USD 0.7 billion to repair damage to US Navy ships.
Trump is currently on a nearly two week-long trip to Indo-Pacific region with North Korea being one of the focus areas during his entire trip.
Trump said his request for an additional USD 4 billion is to support urgent missile defeat and defence enhancements to counter the threat from North Korea.
"This request supports additional efforts to detect, defeat, and defend against any North Korean use of ballistic missiles against the United States, its deployed forces, allies, or partners," the US president said in the communication.
The request also includes costs necessary to repair damage to and restore the operational readiness of the USS John S McCain and the USS Fitzgerald.
"These ships provide critical naval presence and additional ballistic missile defence capabilities in the Asia-Pacific theater," he said.
Trump said his request includes costs associated with increased US troop levels in Afghanistan in support of my Administration's South Asia strategy.
The additional resources would enable Department of Defence to deploy an additional 3,500 troops, and includes funding for urgent needs and special operations forces capabilities.
Trump said that the funding to support the South Asia strategy could be designated as Overseas Contingency Operations.
Republican leaders Senator John McCain and Congressman Mac Thornberry – respective chairmen of the Senate and House Armed Services Committee – welcomed the move.
The additional request would provide resources to support the renewed efforts in Afghanistan and much-needed funding to repair the Navy ships damaged in recent collisions at sea, they said.
"This request also underscores the threat posed by the rogue North Korean regime and the urgent need to boost our missile defence capabilities to meet it," the two Republican leaders said in a statement.
In fact, the House and Senate Armed Services Committees have already authorized many of these missile defence programs in our respective defence bills," they said.
Having completed his first visit to Japan, Trump on Monday landed in South Korea, after which he would travel to China.
Later he would also travel to Vietnam and the Philippines.