Li did not specifically mention the U.S. military "pivot" towards Asia which has concerned China nor Beijing's territorial spats with its neighbors, stressing instead the common interests between the world's top two economic powers.
"Our government will work with the Obama administration to work together to build a new type of relationship between great countries," Li told reporters at a carefully scripted news conference at the end of the annual session of parliament.
"China and the United States should have sound interactions in the Asia-Pacific region and starting from this we can move to build a new type of relationship between powers," he said.
"That will also be good for peace and development in the Asia-Pacific region and the world at large."
Li did not talk about frictions between the two including North Korea's nuclear ambitions and China's claims over the South and East China Seas. Nor did he mention U.S. plans announced on Friday to bolster missile defenses in response to "irresponsible and reckless provocations" by North Korea.
But he did directly address accusations by Washington of hacking from China of U.S. military, government, corporate and media computer systems.
A U.S. computer security company said last month that a secretive Chinese military unit was likely behind a series of hacking attacks mostly targeting the United States.
China has countered on numerous occasions that it too is a victim of hacking attacks.
"I think we should not make groundless accusations against each other, and spend more time doing practical things that will contribute to cyber-security," Li said.
Noting that he "sensed the presumption of guilt" in a reporter's question, Li said called cyber-security a worldwide problem and said: "China does not support, indeed, we are opposed to, such activities."
Obama raised U.S. concerns about computer hacking in a phone call with Chinese President Xi Jinping on Thursday, the same day Xi took office.
U.S. Treasury Secretary Jack Lew will press China to investigate and stop cyber-attacks on U.S. companies and other entities when he visits China this week, a senior U.S. official said on Friday.
Lew will also press Beijing to allow the Chinese currency to rise further against the dollar, and push on other concerns such as increased market access for U.S. goods and better protection of U.S. intellectual property rights, the official said.
New U.S. Secretary of State John Kerry plans to make his first visit to China in coming weeks.
Despite the tensions, both sides have many mutual interests, including ensuring stability on the Korean peninsula and the health of the world economy.
(Reporting by Terril Yue Jones and Benjamin Kang Lim; Editing by Ben Blanchard and Nick Macfie)