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The spokesman said they had also discussed the current deadlock in negotiations between the two countries on China's application to join the World Trade Organisation.
He said Mr Clinton had expressed the view that both sides needed to continue working on this subject.
The American president had already apologised to the Chinese people in public, as well as in a private letter to President Jiang. He had been making efforts to talk to Mr Jiang since last weekend, but the Chinese leader had previously declined to accept the call.
US irritation
The BBC's State Department Correspondent, Richard Lister, says that, in private, many members of the US government are irritated by what they see as China's efforts to use the incident as a political lever.
Beijing has already suspended military exchanges and human rights talks with the United States and is refusing to discuss a peace plan for Yugoslavia until Nato stops its air campaign.
Meeting with ambassador
Earlier, Mr Clinton met the Chinese Ambassador in Washington, Li Zhaoxing, and signed a condolence book for the victims of the embassy bombing.
He also told the ambassador the United States would carry out a full investigation into the bombing and would inform the Chinese people of its results.
German Chancellor Gerhard Schröder was in Beijing this week to make a formal apology to China on behalf of Nato and Germany for the alliance's bombing of the embassy in Belgrade.
Casualties return
Not long after Mr Schröder's arrival, a plane landed in Beijing carrying the remains of the three people who died in the attack, as well as the 20 people who were injured.
After talks with China's Prime Minister, Zhu Rongji, and Foreign Minister, Tang Jiaxuan, Mr Schröder said that he felt his expressions of sympathy had been understood.
Mr Schröder said he had told the Chinese prime minister the bombing was "a tragic accident and nothing else".
Country profiles
Nato apologises to Beijing
(12 May 99 | Asia-Pacific)
Analysis: Beijing's dilemma
(10 May 99 | Asia-Pacific)
US used wrong map for embassy attack
(14 May 99 | Europe)
Clinton apologises for embassy bombing
(10 May 99 | World)
China moves to control protests
(10 May 99 | Europe)
Chinese Ministry of Foreign Affairs
Nato
The White House
US Government
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