Blinken, in China for the second time in less than a year, pointed to improvements in the relationship but urged greater action from Beijing on areas including curbing support for Russia.
Meeting Blinken in Beijing's Great Hall of the People, Xi said the two countries had "made some positive progress" since he met with US President Joe Biden in November.
"The two countries should be partners, not rivals," Xi said.
But he issued a warning over what China considers US pressure to curb its economy, which have included a sweeping ban on semiconductor exports and efforts to wrest blockbuster app TikTok from its Chinese owners.
"We hope the US can also take a positive view of China's development," Xi said.
"When this fundamental problem is solved," he said, "relations can truly stabilise, get better and move forward".
Earlier China's Foreign Minister Wang Yi warned Blinken that US pressure could trigger a "downward spiral".
Wang also warned that the question of self-ruled Taiwan was the "first red line" that must not be crossed in China-US relations.
- Pressure on Russia -
Blinken described his talks with Wang at the Diaoyutai state guesthouse -- which lasted more than five and a half hours -- "extensive and constructive".
He announced that the two countries will in the coming weeks hold their first formal talks on managing artificial intelligence, a rising area of concern as the technology progresses rapidly.
But Blinken sounded a warning on China's support for Russia's "brutal war of aggression" in Ukraine, saying that Beijing -- while stopping short of direct arms exports -- has helped Russia ramp up production of rockets, drones and tanks.
Russian President Vladimir Putin said this week he will visit China in May.
"Russia would struggle to sustain its assault on Ukraine without China's support," Blinken said, warning that the United States was ready to take action against Beijing if it does not take action itself.
But he said China has been helpful in the past, including in discouraging nuclear weapons use by Russia, and said that Wang promised to stay in touch on the Middle East, a key priority for Washington.
Pointing to China's ties with Iran, whose shadow war with Israel has come into the open, Blinken said: "I think the relationships that China has can be positive in trying to calm tensions, to prevent escalation, avoid the spread of the conflict."
- Addressing gaps 'responsibly' -
US officials and experts believe that Xi's foremost priority is to manage headwinds in the Chinese economy and that, at least in the short term, he is looking to avoid flare-ups with the West.
As he opened the meeting with Wang, Blinken said China and the US should manage the relationship "responsibly" and added: "I hope we make some progress on the issues our presidents agreed" on at the California summit.
The two countries should be as "clear as possible about the areas where we have differences -- at the very least to avoid misunderstandings, to avoid miscalculations", Blinken said.
"That really is a shared responsibility that we have not only for our own people, but for people around the world, given the impact that our relationship has," he said.
Biden, who recently spoke by telephone with Xi, faces a tough re-election fight in November against his predecessor Donald Trump, who has cast China as an enemy and vowed a hard line.
The Biden administration has pointed to wins with China, with Blinken highlighting efforts by China to curb precursor chemicals to fentanyl, the painkiller behind an epidemic in the United States.
He said he urged China to carry out further prosecutions.
But while open to cooperation, Biden has increased pressure on China beyond Trump in some areas.
In the latest move, the US Congress, with Biden's support, voted to force the divestment of TikTok from Chinese company ByteDance or risk a ban in the United States.
Blinken said, however, that TikTok did not come up in his talks.
US officials allege security and privacy concerns over the app, which has taken off among US teenagers.
ByteDance denies the allegations and has insisted it has no intention of selling.
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