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With Seoul expecting another North Korean missile test, South Korean warships on Tuesday conducted live-fire exercises at sea, a second-straight day of military swagger from a nation still rattled by the North's biggest-ever nuclear test.

The explosion Sunday, which Pyongyang said was a test of a hydrogen bomb, was a huge advance in the North's push for viable nuclear-tipped missiles capable of hitting the United States. It has also resulted in South Korea boosting its own military capabilities. Washington and Seoul agreed to lift restrictions on South Korean missiles they'd previously agreed upon, according to the South Korean presidential office, allowing for Seoul to improve its pre-emptive strike capabilities against the North.

The Korean Peninsula has been in a technical state of war since the Korean War ended in an armistice in 1953. The near-constant unease has worsened in recent months as the North has displayed rapid improvement in its weapons capabilities, testing intercontinental ballistic missiles and a string of other missiles meant to target U.S. forces in Asia and the U.S. mainland.

More launches may be coming. The Defense Ministry said Monday that North Korea appeared to be planning a future missile launch, possibly of an ICBM, to show off its claimed ability to target the United States with nuclear weapons. It was unclear when such a launch might happen, but Sept. 9 is the anniversary of North Korea's founding and past launches have coincided with important national dates.

South Korean ships including a 2,500-ton frigate, a 1000-ton patrol ship and 400-ton guided-missile vessels participated in the drills aimed at retaliating against potential North Korean provocations, the Defense Ministry said. It plans more naval drills in its southern seas through Saturday. On Monday, Seoul used F-15 fighter jets and land-based ballistic missiles to simulate an attack on North Korea's nuclear test site to "strongly warn" Pyongyang over the recent detonation.

The U.N. Security Council held its second emergency meeting about North Korea in a week on Monday, with U.S. Ambassador Nikki Haley saying the North's actions show that leader Kim Jong Un is "begging for war."

"Enough is enough. War is never something the United States wants. We don't want it now. But our country's patience is not unlimited," Haley said.

The heated words from the United States and the military maneuvers in South Korea are becoming familiar responses to North Korea's rapid, as-yet unchecked weapons progress.

South Korea has been seeking to obtain more powerful missiles for a so-called "kill chain" pre-emptive strike capability to cope with North Korea's growing nuclear and missile threat.

Since the late 1970s, South Korean missile developments have been limited by a bilateral "guideline" between the United States and Seoul. It was updated in 2012 to allow the South to increase the range of its weapons from 300 kilometers (186 miles) to 800 kilometers (497 miles).

An agreement revealed Tuesday removes the 500-kilogram (1,100 pound) warhead limit on South Korea's maximum-range missiles, which would allow the South to potentially target the North's underground facilities and shelters.

North Korea Nuclear Weapon Kim Jong-un
North Korean leader Kim Jong Un provides guidance with Ri Hong Sop (2nd L) and Hong Sung Mu (R) on a nuclear weapons program in this undated photo released by North Korea's Korean Central News Agency (KCNA) in Pyongyang September 3, 2017. KCNA via REUTERS

In addition to expanding its missile arsenal and holding military exercises, South Korea is also strengthening its missile defense, which includes the high-tech Terminal High Altitude Area Defense battery deployed in the southeastern county of Seongju.

North Korea is thought to have a growing arsenal of nuclear bombs and has spent decades trying to perfect a multistage, long-range missile to eventually carry smaller versions of those bombs. Both diplomacy and severe sanctions have failed to check its march to nuclear mastery.

President Donald Trump, asked in Washington if he would attack North Korea, said, "We'll see." No U.S. military action appeared imminent, and the immediate focus appeared to be on ratcheting up economic penalties, which have had little effect thus far.

In tweets earlier this week, Trump threatened to halt all trade with countries doing business with North Korea, a clear warning to China. Such a move would be radical since the U.S. imports about $40 billion in goods a month from China. China called that threat unacceptable and unfair.

Sunday's detonation builds on recent North Korean advances that include test launches in July of two ICBMs, which, when perfected, could target the U.S. mainland. The North also threatened to launch a salvo of Hwasong-12 intermediate range missiles toward the U.S. Pacific island territory of Guam, the home of military facilities the North claims are meant to target it.

The U.S. has about 28,000 troops stationed in South Korea and is obliged by treaty to defend it in the event of war.