The United States is calling North Korea to pursue a "path of peace" following the death of leader Kim Jong-il.
Secretary of State Hillary Clinton said America was ready to help the North Korean people and create lasting security on the Korean peninsula, the BBC reports.
Kim Jong-il died on Saturday of a heart attack, state media reported on Sunday. He was 69.
The US has been holding urgent talks with the communist state's neighbours and president Barack Obama has promised to defend regional allies.
A period of official mourning for Kim Jong-il has begun in North Korea before he is buried on 28 December.
Kim Jong-il had been in the process of formalising his third son, Kim Jong-un, as his successor. But the transition had not been completed and analysts fear Mr Kim's death could trigger a period of instability in the internationally isolated nuclear-armed state, the BBC reports.
Hillary Clinton said America hoped for improved ties with the people of North Korea following Mr Kim's death and was in touch with its partners in the six-party nuclear talks.
"We both share a common interest in a peaceful and stable transition in North Korea," she said in an appearance at the White House with visiting Japanese Foreign Minister Koichiro Gemba.
"We reiterate our hope for improved relations with the people of North Korea."
South Korea, Japan and the US have all spoken about the need for a stable and peaceful transition.
China's president visits embassy
China's president has visited the North Korean embassy in Beijing to express his condolences.
Hu Jintao's visit is seen as a sign of the government's determination to protect its ties with Pyongyang as North Korea enters a new phase, Reuters reports.
The Chinese government has already expressed confidence in Mr Kim's successor, his third son Kim Jong-un.
In the 18 months before his death Kim Jong-il, who rarely travelled overseas, visited China four times.
Impoverished and squeezed by international sanctions for conducting a series of nuclear and missile tests since 2006, North Korea has increasingly turned to Beijing for help to fill the gap left by the drying up of economic assistance from South Korea and the United States.
In turn, China has made clear that it wants to shore up North Korea as a buffer protecting its regional influence from the US and its allies.