Tensions have soared on the peninsula in recent months, with Pyongyang carrying out its first successful tests of an intercontinental ballistic missile (ICBM), bringing much of the USA within range.
But South Korea's new president, Moon Jae-in, appeared to rebuke Trump's threats last week to unleash "fire and fury" on North Korea if it continued making threats.
"President Trump expressed his position to actively support the move", a South Korean government spokesperson said following the conversation between the two heads of government, according to Yonhap News. "So I want all South Koreans to believe with confidence that there will be no war".
In 2005, North Korea reached an agreement with six countries to suspend its nuclear programme in return for diplomatic rewards and energy assistance but the deal later collapsed. "In early May, we got initial intercept capability and they continue to build on that capability", said Manning of the United States moving the defences into South Korea during a transitional period before Moon came to power.
Trump's rhetoric has raised alarm among observers but Moon, who visited Washington at the end of June, declined to criticise his choice of words.
Trump's recent threats followed a report that US intelligence indicates North Korea can now put a nuclear warhead on its long-range missiles.
He added: "All South Koreans have worked so hard together to rebuild the country from the ruins of the Korean War".
"We're all looking to get out of this situation without a war", Dunford said.
The U.S. -North Korea impasse, which has simmered since the end of the Korean War in 1953, has grown more tense in recent months because of worries that the North's nuclear weapons program is nearing the ability to target the U.S. mainland.
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"The most important task at hand is for the USA and North Korea to "hit the brakes" on their mutual needling of each other with words and actions, to lower the temperature of the tense situation and prevent the emergence of an 'August crisis, '" Wang was quoted as saying in the Tuesday conversation.
Beijing has grown increasingly exasperated with its wayward neighbour, but fears instability and the prospect of U.S. troops on its border in a united Korea.
But since coming to power his gestures have been rebuffed by Pyongyang, and he played down the urgency of dialogue.
"But we don't need to be impatient", Moon said.
For talks to take place, he said, "there must be a guarantee that it will lead to a fruitful outcome".
Only then could Seoul consider sending an envoy to the North, he added. Moon urged North Korea not to make further provocations, saying it would face much tougher sanctions that the impoverished country would be unable to withstand if it persists with its nuclear weapons development. "I would tell you that we would be favorably inclined to do anything which furthers the defense capabilities of South Korea and we certainly have seen our alliance change and adapt over time before", Pentagon spokesperson Davis told reporters.
North Korea and the United States exchanged threats of military action last week, with Pyongyang saying it will develop a plan to fire missiles to land in waters near the U.S. Pacific territory of Guam.
The ministry quoted Lavrov as saying tensions could rise again with the USA and South Korea set to start large military exercises on August 21.