"I attach great importance to China's relationship with the United States," Xi, who became China's top leader last week, told Lew, who became U.S. treasury secretary last month, China Daily reported.
The newspaper, quoting analysts, said Lew's two-day visit, to be followed by other high-ranking U.S. officials, demonstrates the United States too has expectations of the new Chinese administration. The new leaders assumed power under the Communist country's once-a-decade leadership transition that began with the party congress last November and ended this month with Xi being elected president. He is already the general secretary of the Communist Party and chairman of the party's powerful military commission.
China Daily said Xi told Lew he wants to build a new type of relationship with Washington centered on core interests. Analysts told the newspaper Xi's stress on "core interests" clarified in a polite but firm way the basis for bilateral ties.
Those present at the Xi-Lew meeting included diplomats and financial officials, including new China's new Finance Minister Lou Jiwei.
A Chinese Foreign Ministry news release quoted Xi as saying China is ready to work with the United States to "respect and take care of each other's core interests and major concerns and properly handle differences" and that China wants to "open a path of new relations between major countries."
The U.S. Treasury Department on its website said topics Lew planned to discuss would include opportunities for cooperation and growth and efforts to level the playing field and create new opportunities for U.S. workers and businesses. Premier Li Keqiang and central bank Gov. Zhou Xiaochuan were among Chinese officials Lew planned to meet.
Other official Chinese media said Lew planned to push China to allow its currency to rise faster against the dollar and to ask China to take steps to increase market access for U.S. goods and to protect intellectual property rights better.
Cyber hacking, another major issue between the two sides, was also expected to be on Lew's agenda.
China's growing assertive claims in the South China Sea and the East China Sea also have become a source of concerns to U.S. officials.
Bilateral trade between the two countries reached a record high of $484.68 billion in 2012, up 8.5 percent year-on-year. However, some U.S. critics have said a lower Chinese yuan allows Beijing to run huge trade surpluses against the United States.
China has become the world's second largest economy after the United States and is also the world's largest exporter.
"Both sides should take an objective look at the other's stage of development, respect each other's development interests, and take each other's opportunities and challenges as their own," Xi said. Chinese demands include Washington lifting its ban on exporting high-tech products to China and having it grant market economy status to China.