The top nuclear envoys of South Korea and the United States share the gravity of the situation on the Korean Peninsula, amid rising tensions caused by North Korea's demolition of a joint liaison office and bellicose rhetoric, a diplomatic source said Sunday.

Seoul's chief nuclear negotiator Lee Do-hoon held talks with his US counterpart, Stephen Biegun, on Thursday during his low-key trip to Washington that followed the North's blowing up of the office in its border city of Kaesong on Tuesday and threats of military action against the South.

Lee returned home Saturday but waved away reporters' questions about his discussions with Biegun.

"Yes, it is a self-evident fact that the situation on the peninsula is grave," the source told Yonhap News Agency, touching on what was talked about during the meeting between Lee and Biegun.

The source refused to further comment on the talks, saying, "Let's wait and see."

Seoul and Washington officials remained low key about the talks between Lee and Biegun, apparently to avoid provoking the North that has berated the South for "servitude and submission" in a swipe at Seoul's policy coordination with the US.

Lee's unannounced trip to Washington despite the COVID-19 pandemic spawned speculation that the two nuclear envoys could explore ways to prevent further escalation of cross-border tensions through cooperation with China or other measures.

In an apparent appeal for China's role to tackle the North Korean issue, David Stilwell, the US assistant secretary of state for East Asia, said Thursday that North Korea seems to be an "obvious" area of cooperation between Washington and Beijing.

"If the US and China can both work together on this, it seems that North Korea would understand the importance and the need to get back to the table and discuss their nuclear program," he said during a briefing on Wednesday's meeting between US Secretary of State Mike Pompeo and Yang Jiechi, a politburo member of China's Communist Party.

In recent weeks, Pyongyang has been ratcheting up tensions, taking umbrage at Seoul's "connivance" of North Korean defectors and activists sending anti-Pyongyang leaflets into the North.

The South Korean military has been keeping tighter vigilance amid the possibility of North Korean provocations, such as a submarine-launched ballistic missile test. (Yonhap)