The two leaders met here on the eve of a resumption of talks in Beijing aimed at persuading North Korea to abandon its nuclear weapons.
Mr. Bush said his discussions with Hu ranged from how to prevent an avian flu pandemic to economic matters and feared nuclear proliferation in North Korea and Iran. He seemed pleased when Hu said, "We stand ready to step up our communication and cooperation" to gain fresh progress in negotiations with North Korea.
Without elaboration, Mr. Bush said he planned to raise human rights abuses in China with Hu. For his part, Hu bluntly asked Mr. Bush to "join the Chinese side in safeguarding peace and stability across the Taiwan Strait" and said "it is inevitable that we may have some frictions" over trade as Beijing has a massive surplus.
Mr. Bush met with Hu at the end of a busy day of diplomacy stretching from the White House to the United Nations. The president, at a news conference in Washington, issued a stern warning to Syria about alleged involvement in Iraq and vowed the United States will not waver from its commitment in Iraq.
Consumed by Hurricane Katrina recovery efforts for two weeks, Mr. Bush pivoted to foreign policy for a meeting of more than 160 presidents, prime ministers and kings at a summit on combating poverty and reforming the United Nations. Mr. Bush is to address the General Assembly on Wednesday.
Mr. Bush has had a testy relationship with the U.N., portraying it as a bloated bureaucracy slow to address global problems. Criticism of the United States is common, particularly over the war in Iraq and Mr. Bush's refusal to sign the Kyoto treaty on global warming.
Mr. Bush arrived here with the lowest approval ratings of his presidency and the perception that his administration had mishandled hurricane relief. He said he took responsibility for whatever had gone wrong.
Mr. Bush met privately in a hotel suite with Hu, making his first visit to the United States as his country's leader. The White House is concerned about China's growing economic and military might and its voracious thirst for oil, a factor in rising U.S. gasoline prices.
The Mr. Bush administration is seeking the support of China, Russia and India to bring Iran before the U.N. Security Council for possible sanctions for its suspected nuclear weapons program.
Iran suspended uranium conversion and enrichment activities last year but resumed them last month. Iran's foreign minister, Manouchehr Mottaki, warned of serious consequences if the Security Council considers sanctions.