(CNN) US President Donald Trump said he was sending "an armada" to Korean waters to potentially deal with threats from Pyongyang.

But its no-show has caused some South Koreans to question his leadership and strategy regarding their unpredictable neighbor in the north.

And as the country prepares to vote for a new president on May 9, the claim could have far-reaching implications for the two countries' relations.

"What Mr. Trump said was very important for the national security of South Korea," Presidential candidate Hong Joon-pyo told the Wall Street Journal

"If that was a lie, then during Trump's term, South Korea will not trust whatever Trump says,"​ said Hong, who is currently trailing in the polls.

South Korean media also seized on the conflicting reports on Trump's "armada" -- led by the aircraft carrier USS Carl Vinson.

The aircraft carrier USS Carl Vinson in the Sunda Strait, Indonesia, on April 15.

One newspaper headline called it Trump's "Carl Vinson lie," and speculated that the Russian and Chinese leaders must have had a good laugh at its absence.

Meant to present a robust defense against a potential nuclear test by Pyongyang, the report likened the bluff to North Korea's shows of force, where "fake missiles" are paraded through the streets of the North Korean capital.

"Like North Korea, which is often accused of displaying fake missiles during military parades, is the United States, too, now employing 'bluffing' as its North Korea policy?" it asked.

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Sending the armada

In the face of antagonism from North Korea last week, Trump had said the USS Carl Vinson carrier group was being deployed to waters off the Korean Peninsula.

"We are sending an armada. Very powerful," Trump told Fox Business Channel's Maria Bartiromo. "We have submarines. Very powerful. Far more powerful than the aircraft carrier. That, I can tell you."

It turns out the carrier group was never actually steaming towards the peninsula, but rather heading to joint exercises with the Australian navy. US officials insist it's now on its way to the Sea of Japan, known in South Korea as the East Sea. It still hasn't arrived

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On Thursday, the US Navy announced it was extending the Vinson's deployment by 30 days "to provide a persistent presence in the waters off the Korean Peninsula."

South Korea reacts

If Trump's initial declaration was a bluff, it appears to have worked. The anticipated North Korean nuclear test didn't materialize.

But questions remain over the efficacy of the tactic over time.

"I understand strategic ambiguity for military authorities. However, it's different (for a) political leader," Yang Moo-jin, of the University of North Korean Studies, told CNN.

"Trump, (Vice President Mike) Pence and (Secretary of Defense James) Mattis all used this to raise tension and pressure North Korea. Strong nations' power comes from transparency, not the opposite.

"How does the US expect South Koreans to trust the US when its leader bluffs and exaggerates? South Koreans' feelings were hurt considerably by remarks by the leader of a close ally."

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Confusion reigns

Trump's initial assurance, in the form of a strong military response, telegraphed a robust defense of the US' stalwart allies, South Korea and Japan.

It also ratcheted tensions on the peninsula, prompting North Korea's deputy ambassador to the UN to warn that the US was risking nuclear war with its actions on the peninsula -- any hostile act is inherently a dangerous calculation when dealing with an unstable actor like North Korean leader Kim Jong Un.

A senior administration official later said a miscommunication between the Pentagon and the White House was to blame for the mixed reports.

White House press secretary Sean Spicer, however, compounded the confusion , by doubling down on the President's assertions.

"We have an armada going toward the peninsula. That's a fact," he told a skeptical press corps during his daily briefing on Wednesday, arguing that, in the broadest sense, the president's statement was accurate because the ships would eventually get to the waters between North Korea and Japan.

Meanwhile, the US and South Korean military are currently engaged in joint training exercise at the Kunsan Air Base on the west coast of the Korean Peninsula. North Korea has long objected to the two countries' annual joint maneuvers.

"We've been tasked to do these yearly exercises because we always have to be ready to defend the republic of Korea and we've been doing it obviously for a while and we will keep doing it as need be," Lt. Col. Steven Raspet told CNN.

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Political thin ice

The bluff -- if that is what it was -- comes at a precarious time for South Korean politics -- in less than a month, the country will go to the polls to elect a replacement for impeached President Park Geun-hye.

In addition to the comments about US-South Korea relations made by Hong, the presidential candidate from Park's ruling party, the confusion over the US' response to the potential nuclear tests has led to questions about how much the government and the military knew about the location of the Vinson and its group.

Questions about what this means in the context of the election, where Pyongyang's increased belligerence has been a key election talking point, abound.

"Both South Korea and the US are in close cooperation to deter North Korea's provocations and to pursue peace and stability of the Korean peninsula," a South Korean Defense Ministry official said.

"The defense ministry has been and is closely working together with the US military. However, it is inappropriate for the ministry to go into details about the (strength of the) US military operation."

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Wounded pride

Some of Trump's comments have also rankled in South Korea. He told the Wall Street Journal -- after getting a primer on regional geopolitics from Chinese President Xi Jinping -- that the Korean peninsula "actually used to be part of China."

South Korea's Foreign Affairs Ministry, in a daily briefing Thursday, announced the government's response to the comments.

"The Ministry is in the process of checking facts with both the US and China through various diplomatic channels," the ministry's spokesperson Cho June-hyuck said.

"The international community unequivocally acknowledges that Korea was never a part of China in its thousands of years of history that no one can deny the fact," he added.