By Gordon Lubold and  Jonathan Cheng

WASHINGTON—The Pentagon on Tuesday conducted a successful test of a system designed to shoot down an intercontinental ballistic missile, U.S. defense officials said, a demonstration that came amid rising tensions over North Korea’s nuclear weapons program.

The successful missile-defense test marked the second U.S. military display in as many days, following a joint U.S. and South Korean exercise on Monday in which U.S. B-1B bombers flew near the Military Demarcation Line that divides North and South Korea. The Monday flyover came just hours after North Korea test-launched a short-range missile, its third launch in less than three weeks and one that it claimed was more precise than any it has fired.

Both the B-1 bomber flyover and Tuesday’s U.S. missile-defense test were previously scheduled, but have taken on an air of urgency and immediacy in light of North Korea’s continued testing of missiles and warheads with a goal of reaching the continental U.S.

The Pentagon said that in Tuesday’s test, it successfully intercepted a mock weapon launched from a site on Kwajalein Atoll in the Marshall Islands. A U.S. “interceptor” was fired from Vandenberg Air Force Base, Calif., interrupting the flight of the mock ICBM over the Pacific Ocean, according to defense officials.

Officials said Tuesday marked the first live-fire test on a target closely resembling the characteristic of an ICBM.

“This test demonstrates that we have a capable, credible deterrent against a very real threat,” said Vice Adm. Jim Syring, director of the Missile Defense Agency, in a statement.

Capt. Jeff Davis, a Pentagon spokesman, said that while the test wasn’t timed to the current tensions in North Korea, “in a broad sense, obviously, North Korea is one of the reasons why we have this capability.” He also named Iran as a concern.

President Donald Trump has vowed that North Korea won’t achieve the capability of launching a nuclear missile able to reach the U.S. He has turned to China in a diplomatic effort to head it off, while also establishing an increasing American military presence in the region.

However, the Trump administration’s strategy of pressure and military threats has run into complications from South Korea’s new president, Moon Jae-in. The new leader has said he wants to seek greater engagement with the North and has questioned some of Seoul’s cooperation with Washington.

On Tuesday, Mr. Moon said he was demanding an investigation of a mobile missile-defense system known as the Terminal High Altitude Area Defense system, or Thaad, installed by the U.S. in South Korea. Mr. Moon said during the presidential campaign in the spring that he would review the process under which the previous administration agreed to install Thaad, which is fiercely opposed by China, but he appears to have softened his view amid continued North Korean missile launches.

On Tuesday, however, Mr. Moon said that his defense ministry didn’t inform him that four more launchers had been brought into South Korea in addition to two existing ones that had been previously announced, calling the discovery “very shocking,” according to a spokesman for the presidential office.

U.S. officials didn’t respond to a request for comment on Mr. Moon’s assertion, but Capt. Davis, the Pentagon spokesman, said Tuesday that the Thaad deployment process had been “very transparent.” Similar U.S. mobile systems contain six launchers.

Separately, Mr. Moon said in a phone call with Japanese Prime Minister Shinzo Abe that he supported more pressure and sanctions on North Korea after the latest missile test and that “now is not the time for dialogue” with Pyongyang, according to his spokesman. The message was an apparent hardening of his position on North Korea.

Two weeks ago, Pyongyang test-fired a missile that it later called the Hwasong-12, which analysts said could fly 2,800 miles—considerably farther than its previous missiles and far enough to reach the U.S. military base on Guam. About a week later came the Polaris-2 missile, fueled by a solid rather than a liquid fuel—meaning it requires much less time to prepare for launch, giving Pyongyang more flexibility and stealth. That could pose more of a challenge to missile-defense systems.

Tuesday’s U.S. exercise tested what is known as the ground-based midcourse defense system, or GMD, one of four main antimissile system components. Others include U.S. Aegis warships, the Thaad mobile launchers and Patriot batteries.

Officials said initial indications were that the test “met its primary objective,” but that experts would more closely evaluate the system’s performance.

The test drew praise from a key lawmaker. “This is a tremendous success for Adm. Syring and his team,” said Rep. Mike Rogers (R., Ala.), chairman of the House Armed Services Committee’s subpanel on strategic forces. “The dictator in North Korea surely understands that the United States will not allow itself or its allies to be subject to his threats.”

The U.S. now has conducted 17 tests of the ground-based missile defense system, and nine have succeeded, according to the Missile Defense Agency.

There was no immediate reaction from North Korea, but Pyongyang condemned Monday’s B-1 bomber flight by the U.S. and South Korea.

“The U.S. imperialists’ ever-more reckless military provocation clearly proves that their talk about ‘dialogue’ is nothing but hypocrisy to disarm the DPRK and their wild ambition to eliminate the DPRK with nukes remains unchanged even a bit,” it said, using the acronym for North Korea’s formal name, the Democratic People’s Republic of Korea.

North Korea accused the U.S. of staging a “nuclear-bomb-dropping drill” with the bombers, which it sees as a new provocation in addition to the presence of the USS Carl Vinson and the USS Ronald Reagan, two aircraft carriers that are operating near the Korean Peninsula.

Tuesday’s missile-defense test came as Mr. Trump and his foreign policy and national security team grapple with how to counter North Korean leader Kim Jong Un’s behavior.Mr. Kim has launched a series of test missiles into the Pacific, but has yet to test an intercontinental-range missile capable of reaching the continental U.S.

The last test of the ground-based system, in June 2014, was successful, but three tests before that—in July 2013, December 2010 and January 2010—all failed.

The causes of the failures, according to the missile agency, ranged from technical problems involving software and sensors to major faults such as a rocket booster failing to separate from the “kill vehicle,” the term for the part of the interceptor that zeroes in on the incoming missile, according to defense officials.

The Defense Department has logged better results from tests involving the ship-based system and Thaad launchers. A compilation earlier this year showed that, overall, the military succeeded in 75 of 92 missile-defense tests since 2001.