But US hopes that China would commit itself to supporting the zero option for the nuclear test-ban treaty being negotiated in Geneva, under which tests even on a tiny scale would be outlawed, were disappointed. Nor did Mr Clinton offer any promise to Mr Jiang to refuse outright further visits to the US by Taiwan's leaders.
Earlier, Mr Jiang used a speech at the 50th-anniversary celebration of the UN to deliver a sharp jab at the US, criticising "big powers" that seek to interfere in the internal affairs of other countries.
US-Chinese relations took a downturn in spring, when Mr Clinton allowed President Lee Teng-hui of Taiwan to make a private visit to the US. Strains have also arisen because of China's treatment of dissidents, including Harry Wu, a US citizen convicted of spying and stealing state secrets before being deported in August.
"The peaceful reunification of the two sides of the Taiwan straits is the unshakeable will and determination of the entire Chinese people," Mr Jiang said. In a television interview this week he reiterated that "one cannot rule out the military option" against Taiwan.
But in remarks that appeared to be directed at the US and its efforts in the past to link trade with progress on human rights, Mr Jiang said: "Certain big powers, often under the cover of 'freedom', 'democracy' and 'human rights', set out to encroach upon the sovereignty of other countries, interfere in their internal affairs and undermine their national unity and ethnic harmony. This has become a principal cause for the intranquillity in the world today."
After the summit, the US Under-Secretary of State for East Asia, Winston Lord, said there had been a "step forward" in relations, but added: "I wouldn't want to suggest there are not problems remaining. There are some serious problems."
On human rights, Mr Clinton raised some specific cases with Mr Jiang. He also reiterated that the US would not support Chinese membership of the World Trade Organisation unless it came forward with a new offer on opening its markets. "We believe that China has not yet made a sufficient offer," Mr Lord said.
Many passages in Mr Jiang's speech were unlikely to sit well with those seeking freedom for Tibet, including Tibetan nationalists who have been on a hunger strike at the UN building. Mr Jiang sought to condemn governments that "deliberately ignore the colourful and diverse reality of the world and practise such hegemonic acts as imposing one's social system" on other nations.