South Korean President Moon Jae-in said on Wednesday there was a "high possibility" of conflict with North Korea, which is pressing ahead with nuclear and missile programmes it says it needs to counter USA aggression.
According to the official Xinhua news agency, Xi told Lee: "China is willing to strengthen communication with the new South Korean government..."
However, South Korea downplayed the progress.
Moon's comments are similar to those made by President Donald Trump in late April.
Despite the push for a tougher stance, Haley held out the prospect of direct talks with North Korea, saying "we are willing to talk but not until we see a total stop of the nuclear process and of any test there".
Moon, a liberal, favors a softer approach to North Korea than his conservative predecessors and has offered to visit Pyongyang if the circumstances are right.
The paper also falsely claimed South Korean protesters were calling for the ouster of former President Park Geun-hye during their weekly "candlelight vigils" because of Park's conservative North Korea policy.
Haley said the Security Council is going to send a strong and unified message to North Korea that "the worldwide community wants to support you but as long as you test, and as long as you continue your nuclear program, you are on an island by yourself".
Communications were severed by North Korea past year, Lee said, after new global sanctions were imposed in response to its fifth nuclear test and Pyongyang shut down a joint industrial zone.
Growing tension caused by North Korea's nuclear weapons program and development of long-range missiles some day capable of carrying nuclear warheads as far as the USA and Canada has worsened significantly due to increased tests carried out by Pyongyang despite United Nations sanctions and demands by Washington that such tests must stop.
"First, the ultimate goal is to completely dismantle the North Korean nuclear weapons", Yoon Young-chan, the spokesman for South Korean President Moon Jae-in, explained. The allies agreed that dialogue with North Korea could happen under the "right conditions," Yoon said. Pyongyang defends its weapons programmes as necessary to counter US hostility and regularly threatens to destroy the United States.
"As Washington has made clear that they will not interfere with Pyongyang's system, now would be an ideal time for North Korea to start talks".
North Korea's test launch on Sunday flew higher and longer than previous tests, leading some experts to believe it could be the country's most advanced launch to date.
"We're not going to continue to just say go ahead and test as often as you want", Haley said, flanked by the South Korean and Japanese ambassadors.
North Korea has carried out two atomic tests and dozens of missile launches since the beginning of past year in its quest to develop a missile capable of delivering a nuclear warhead to the continental United States.
"More importantly", he added, it "may represent a substantial advance to developing an intercontinental ballistic missile".
China has been infuriated by the US deployment of an advanced Terminal High Altitude Area Defense (THAAD) anti-missile system in South Korea, saying it was a threat to its security and would do nothing to ease tension with North Korea.