Winding up a whirlwind round-the-world trip, the new secretary of state's last stop in Peking was the most challenging, attempting to set the tone for the next phase of the volatile Sino-US relationship just days after the death of the former patriarch, Deng Xiaoping.
Yesterday, Ms Albright became the first senior foreign diplomat since Mr Deng's death to meet President Jiang Zemin, the prime minister, Li Peng, and the foreign minister, Qian Qichen, whom she described as all in "deep mourning".
A US official said Mr Jiang was "quite sombre, appropriately so". However, the oficial added: "I thought he looked quite confident, and quite sure of himself."
In a rare indication that the Chinese president might partly write his own speeches, the official said: "President Jiang talked at length about the legacy of Deng Xiaoping, about the memorial service, and the fact that he would be giving the primary address, and how hard he'd been working on it and how much he'd been thinking about it."
Ms Albright said she had expected that her visit would be cancelled, coming as it did on the day Mr Deng was cremated and on the eve of this morning's memorial gathering.
The fact it went ahead was "a very important sign of their desire to pursue the US relationship and the continuity within it", she said.
Ms Albright was scheduled to fly out of China early today so as to be out of the country before the start of the memorial service for Mr Deng, to which no foreign dignitaries have been invited.
The Secretary of State said she had been received "with the greatest kindness and interest", but there was clearly little time for any substantive progress on the many problems - human rights, market access, Taiwan, weapons sales - which beset the bilateral relationship. However, the improved tone set towards the end of last year has continued.
"I am confident, based on today's meetings, that the vigorous strategic dialogue that is developing between the US and China will continue," said Ms Albright, confirming that the US Vice-President, Al Gore, will visit Peking next month.
A summit between Mr Jiang and President Bill Clinton is likely before the end of the year, if the Chinese political situation remains stable.