The drills coincided with military exercises held by United States and South Korean navies in the Yellow Sea, off the western coast of the Korean Peninsula and as the USS Michigan, one of US's most powerful submarines, arrived in South Korea.
South Korea's Joint Chiefs of Staff said they are closely watching North Korean military action in the Wonsan city area, where the drills are reportedly being held.
On Monday (local time) Trump called for tougher new United Nations sanctions on Pyongyang, saying the North was a global threat and "a problem that we have to finally solve".
Meanwhile, in the U.S., every member of the Senate was called to a White House briefing on the threat posed North Korea last week.
Japan's envoy on North Korea, Kenji Kanasugi, said after talks with his US and South Korean counterparts that they all agreed China should take a concrete role to resolve the crisis. "People put blindfolds on for decades and now it's time to solve the problem".
Trump sent the USS Carl Vinson aircraft carrier strike group for exercises off the Korean peninsula as a warning to Pyongyang, but US officials say sanctions, not military strikes, are the preferred option.
A "national meeting" of thousands of senior military and civilian officials was held the day before, although North Korean leader Kim Jong Un did not attend.
Meanwhile, Trump has summoned all 100 senators to the White House for a special briefing leading to speculations that he may start the World War 3.
Japanese officials say USA representative for North Korea Policy Joseph Yun met Tuesday with his Japanese counterpart Kenji Kanasugi and Kim Hong-kyun of South Korea to share their latest analyses and discuss cooperation.
U.S. State Department spokesman Mark Toner said North Korea had become a "front and center front-burner issue" and Tillerson would be "very vocal" on Friday about his concerns that countries were not doing enough to implement sanctions.
North Korea was referring to the date of North Korea's test of a rocket engine that could be used in the launch of an intercontinental ballistic missile.
Armed with tactical missiles and equipped with superior communications capabilities, the MI is one of four U.S. Navy subs that began service as a ballistic missile submarine, loaded with nuclear missiles as part of the U.S. strategic nuclear deterrent.
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In a phone conversation with Trump on Monday, Chinese President Xi Jinping called for all sides to exercise restraint.
The moves to set up THAAD within this year have angered not only North Korea, but also China, the country that the Trump administration hopes to work with to rid the North of nuclear weapons.
Another daily, the JoongAng Ilbo, wrote an editorial saying Seoul shouldn't be left out from important discussions involving North Korea as "the destiny of our nation could be at stake". Alternatively, a long-range missile test could show North Korean progress toward being able to fire a weapon at America.
While the North fired weapons near the east coast of the Korean Peninsula, the USA and South Korea conducted drills off the west coast.
US Vice President Mike Pence said Saturday that the Vinson and its strike group would arrive in the Sea of Japan (East Sea) - which sits between the Korean peninsula and Japan - "in a matter of days". "North Korea is a big world problem, and it's a problem we have to finally solve".
The US ambassador to the UN, Nikki Haley, told American television on Monday that the Chinese pressure on North Korea was working. She praised China's increased pressure on North Korea.
The navies of Japan and South Korea are simultaneously conducting drills with their US counterparts, the US Navy announced in a press release.
Kim said they discussed ways to get more co-operation from China and Russian Federation, which they agreed is crucial to applying effective pressure on North Korea to abandon its nuclear weapons program.
Trump also spoke to Japanese Prime Minister Shinzo Abe on Monday, discussing the joint drills under way between the USA carrier Carl Vinson and Japan's Maritime Self-Defence Force.
"We believe China has a very, very important role to play", said the USA envoy for North Korea policy, Joseph Yun.
Although a major event around the anniversary was viewed as possible, the morning came and went without any nuclear tests or ballistic missile launches.
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