US President George Bush has called on China to expand its social, political and religious freedoms.
On a visit to Beijing, he also said he and his Chinese counterpart Hu Jintao had agreed to work together to reduce their trade imbalance.
Earlier, he attended a service at one of the few officially-recognised Christian churches in Beijing.
The White House said Mr Bush - a devout Christian - wanted to show his support for expressions of faith in China.
The two leaders met for talks at the Great Hall of the People on the edge of Beijing's Tiananmen Square.
It comes at a time of tension over the effect of cheap Chinese imports on US manufacturing.
Mr Hu said they had expressed their willingness to "join hands together to gradually achieve a balance of trade" between the two countries.
"The frictions and problems that may arise in this rapid development of the two-way trade may be properly addressed through consultations," he added.
He also promised to "unswervingly" press ahead towards a more market-based currency. Washington says the yuan is undervalued to boost China's exports at the expense of jobs elsewhere.
And Mr Hu said China was willing to take action to end the illegal copying of goods which the US businesses say cost them billions of dollars.
Mr Bush said a relationship with China was important to the US, and he invited Mr Hu to make the visit he had to postpone in September because of Hurricane Katrina.
Before the talks, a US aide said China was to buy 70 Boeing aircraft.
Correspondents say the purchase may be an attempt to soothe American frustration over China's trade surplus, which is tipped to hit $200bn this year.
Earlier, a key Bush aide said Mr Bush would speak to the Chinese leader about "giving more opportunities for Chinese citizens to worship and speak freely".
On Sunday morning, Mr Bush attended the Gangwashi Church - one of five officially recognised Protestant churches in Beijing - accompanied by his wife Laura.
Mr Bush attended church to show his support for China's Christians
He wrote in the church guest book: "May God bless the Christians of China."
"My hope is that the government of China will not fear Christians who gather to worship openly," Mr Bush told reporters afterwards.
"A healthy society is a society that welcomes all faiths."
The BBC's Rupert Wingfield-Hayes in Beijing says Mr Bush's tone was encouraging rather than lecturing - showing a conscious effort to address the issue without alienating the Chinese leadership.
While on the Japanese leg of his regional tour, Mr Bush urged China to allow more political freedom and pointed to Taiwan - considered a renegade province by Beijing - as a model of a society that has successfully moved from "repression to democracy".
But a spokesman in Beijing said the Chinese "enjoy all forms of democracy and freedom under law".
Mr Bush is nearing the end of his East Asia tour. He flies to Mongolia on Monday.