About 12,000 US personnel and 230 aircraft will take part in the drill.
USA policy, he said, is "to deny North Korea the capability to hit America with a nuclear-tipped missile".
"There are ways to address this problem short of armed conflict, but it is a race because he's getting closer and closer, and there's not much time left".
But even some Trump advisers say United States military options are limited when Pyongyang could launch an artillery barrage on the South Korean capital Seoul - only around 50 kilometres from the border and home to 10 million people.
The missile's large size was immediately apparent in the photos, which analysts said could provide for a more powerful propulsion system.
North Korean monitoring group 38 North said the tremors could be an indication of "Tired Mountain Syndrome" - a condition where rock becomes increasingly permeable following a below-ground nuclear blast.
But it is the stealth fighters that experts say pose the biggest threat to Pyongyang.
Graham said he has had extensive discussions with the Trump administration about the situation.
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Meanwhile, influential Democratic lawmaker Tulsi Gabbard termed as "ridiculous" the release of Hafiz Saeed from house arrest. They (LeT) are the biggest force, India got them declared as terrorists by partnering with United States , " he added.
The initial analysis shows Tuesday's launch likely involved a two-stage missile with a non-explosive dummy warhead, the official said.
"It is an open, all-out provocation against the DPRK, which may lead to a nuclear war any moment", it continued.
To celebrate the missile launched last Wednesday, the ruling Workers Party's official daily Rodong Sinmun covered its front page with color photographs showing thousands of tightly packed soldiers and people applauding in Pyongyang's Kim Il-Sung square, which was decorated with large portraits of the North's late leaders.
It is likely the ballistic missile, fired higher than any previous North Korean missile, broke up as it re-entered Earth's atmosphere, the official said.
South Korea's military believes that the latest missile, which flew 950 kilometers before splashing down in waters near Japan, is potentially capable of striking targets as far as 13,000 kilometers, which would put Washington within reach.
China should take unilateral action to cut off North Korean oil imports, McMaster said, adding, "you can't shoot a missile without fuel".
"We're asking China not to do us or anybody else a favor", he said.