The two countries should think creatively to build such a new type of relationship, he said.
The dialogue began amid controversy over the blind Chinese activist Chen Guangcheng seeking shelter in the US embassy in Beijing as well as tensions between Philippines and China over disputed islands.
US officials escorted Chen out to a hospital on Wednesday. China demanded an apology for the embassy for sheltering him.
Also Philippines and Chinese naval vessels are currently patrolling the disputed waters of an island in the South China Sea in a stand off and Manila sought Washington's assistance to counter Beijing's moves.
In his speech, Hu recalled how former US President Richard Nixon's visit to Beijing changed the bilateral ties 40 years ago and said that both sides need to advance the relationship with the times with new thinking, policies and actions.
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