Also, there is a report from the Korea Times quoting an unnamed South Korean presidential official that the U.S. is considering sending more military equipment to the Korean Peninsula, including stealth fighters, B-1B and B-52 bombers, as well as warships such as U.S. Navy destroyers and submarines.

South Korean media are reporting the two will discuss South Korea's request to double its ballistic missile firepower to counter the rising threat from nuclear-armed North Korea.

Defense Secretary James Mattis is scheduled to hold a previously scheduled bilateral meeting on Wednesday at the Pentagon with Song Young-moo, South Korea's defense ministry.

"The North Korean government has in the past has tended test its missiles and nukes on days of historic significance in North Korean state history or alternatively to thumb their nose at the United States and do it on July 4 or do it on a South Korean national holiday," said Nicholas Eberstadt, who holds the Henry Wendt Chair in Political Economy at the American Enterprise Institute, a conservative think tank.

Experts say fine tuning the nuclear warhead miniaturization on the missiles is one reason the North Koreans want to continue testing nuclear weapons. They say it's possible the regime could do the test on a national holiday such as Sept. 9, the communist state's independence day.

"It's always difficult to predict what the North Koreans will do, but they've been talking about things that would almost certainly require more nuclear testing – including talking about hydrogen bombs," said Matthew Bunn, a nuclear proliferation expert and professor of practice at Harvard University's John F. Kennedy School of Government.

Also, there is speculation the secretive North Korean regime led by Kim Jong Un may be preparing to conduct its sixth nuclear test.

More U.S. military might could be headed for the Korean Peninsula as tensions grow following several North Korean missile launches in the past week.

A U.S. Air Force B-52 Stratofortress, part of the country's nuclear triad, is capable of carrying 70,000 pounds of nuclear or precision guided conventional bombs.

The U.S. Marine Corps has F-35B variant stealth fighters stationed in Japan, and eight previously went to South Korea for training exercises. The nearest B-1B bombers are stationed at Andersen Air Force Base in Guam.

A U.S. defense official told CNBC on Tuesday the military is continuing to closely monitor the developments on the Korean Peninsula, but the official provided no confirmation on the reports that more military hardware could be headed to the region.

In a statement Tuesday, President Donald Trump blasted Pyongyang and said its "threatening and destabilizing actions only increase the North Korean regime's isolation in the region and among all nations of the world. All options are on the table."

On Monday, North Korea launched a ballistic missile over Japan's northern island of Hokkaido. In response, the South Korean government said four fighter jets from its air force staged live-bomb drills in a show of force near the border.

"No country should have missiles flying over them like those 130 million people in Japan," U.S. Ambassador to the United Nations Nikki Haley told reporters Tuesday.

Haley said the dynastic regime led by the 33-year-old dictator has "violated every single U.N. Security Council resolution that we've had and so I think something serious has to happen."

Monday's missile firing over Japan followed North Korea firing a series of missiles on Saturday. The U.S. military indicated there were at least three missiles, including on that appears to have blown up immediately.

David Wright, co-director and senior scientist at the Union of Concerned Scientists, wrote in a blog posting Tuesday that the ballistic missile fired Monday appeared to be a Hwasong-12, similar to one tested May 14. He said the range of the missile is about 4,800 kilometers (3,000 miles), but given it only flew a distance of about 1,700 miles might indicate the regime used a heavier payload than the previous test.

According to Wright, another reason the missile may have flown a shorter distance is due to the North Koreans purposely reducing the range or the "possibly due to a mechanical problem."

The missile firing comes as the annual joint U.S.-South Korean Ulchi-Freedom Guardian military exercises continued this week. The military exercises, which started Aug. 21, are scheduled to continue through Thursday. More than 20,000 forces are participating in the war games, including some U.S. service members brought in for the exercises from off-peninsula.

Earlier this month, North Korea threatened to lob its Hwasong-12 intermediate-range ballistic missiles toward U.S. military bases on the U.S. Pacific territory of Guam. Experts said the test that flew over Japan was more proof the regime's Hwasong-12 can strike Guam.

At the same time, some believe the North may have felt they had to do something given the huge military exercises that are underway right now in South Korea.

"We have ongoing large-scale exercises that they don't like," said Joel Wit, senior fellow at the U.S.-Korea Institute at Johns Hopkins School of Advanced International Studies and co-founder of Washington's 38 North think tank. "To think that they will remain totally silent and totally quiet while that's happening is just ridiculous."

Wit said missile firings and another nuclear test are just some of the ways Pyongyang may vent its anger. He said they also have resorted in the past with other actions, including demilitarized zone landmine provocations.

"The administration is trying to maintain the appearance that a military option is viable," said Wit. "The dirty little secret is it's not viable – and I think Steve Bannon sort of let that secret out before he left."

In an interview published August 16, Trump's chief strategist, Steve Bannon, reportedly told the American Prospect that: "There's no military solution [to North Korea's nuclear threats], forget it." The White House announced August 18 that Bannon no longer worked in the administration.

The Trump administration has been relying on a policy of "maximum pressure" on North Korea, including economic sanctions, as well as leaving the door open to engagement with the hermit regime. But some critics suggest the sanctions still are insufficient and more should be done.

"What they won't stop despite engagement, or with engagement, is the march towards nuclear option," said AEI's Eberstadt. "The idea that we can charm Kim Jong Un out of his nuclear arsenal I think is a little far fetched."

Eberstadt said secondary sanctions maybe needed on Chinese financial institutions and others to further tighten the screws on Pyongyang.

"The U.S. still has a lot of leverage that we can put on China, Russia and other governments whose entities traffic with North Korea," he said. "Because we can just say you can't do dollar-denominated commerce and that's more than a trivial inconvenience."

WATCH: China's trade ties to North Korea