Sullivan, the first US national security advisor to visit China since 2016, met Xi as he wrapped up three days of talks in Beijing which also saw him sit down with Foreign Minister Wang Yi and other high-ranking officials.
His visit came as China was embroiled in security rows with US allies Japan and the Philippines.
Sullivan told Xi during a meeting on Thursday in Beijing's ornate Great Hall of the People that Biden "looks forward to engaging with you again in the coming weeks".
"President Biden is committed to responsibly managing this consequential relationship to ensure that competition does not veer into conflict or confrontation, and to work together where our interests align," he said.
Chinese state media said Xi told Sullivan that in spite of "great changes", China and the US could still enjoy good ties.
"China's commitment to the goal of stable, healthy, and sustainable development of China-US relations hasn't changed," Xi said.
"We hope that the US will work with China to meet each other halfway," he added, according to CCTV.
Sullivan told reporters at the US embassy on Thursday that the talks with Chinese officials had lasted for 14 hours, describing the discussions as "constructive, candid, substantive".
The Ukraine war came up during the talks, but Sullivan said that both sides had not reached "any particular plan".
"I can't say that we did make progress on that issue," he said.
The talks did not touch on the upcoming US election, but Sullivan said that Vice President Kamala Harris wanted to maintain "open lines of communication" with China.
Harris, also the Democratic presidential nominee, "shares President Biden's view that responsibly managing this competition so it doesn't veer into conflict or confrontation is essential", Sullivan said.
On Wednesday, Sullivan and top diplomat Wang had discussed plans for their leaders to talk in the coming weeks.
They also clashed over China's increasingly assertive approach in disputed maritime regions.
- Taiwan 'red line' -
On Thursday morning, Sullivan met with senior Chinese army official Zhang Youxia at the Beijing headquarters of the Central Military Commission, where the two discussed Taiwan and other flashpoint issues.
"It's rare that we have the opportunity to have this kind of exchange," Sullivan told Zhang in opening remarks.
The officials agreed to hold a call between the two sides' theatre commanders "in the near future", a readout from the White House said.
Sullivan also raised the importance of "freedom of navigation" in the South China Sea, where China and the Philippines have clashed in recent months, and "stability" in the Taiwan Strait, Washington said.
Zhang, in turn, warned that the status of the self-ruled island was "the first red line that cannot be crossed in China-US relations".
"China has always been committed to maintaining peace and stability in the Taiwan Strait," he said, according to a readout by Beijing's defence ministry.
"But 'Taiwan independence' and peace and stability in the Taiwan Strait are incompatible," he said.
"China demands that the US halts military collusion with Taiwan, ceases arming Taiwan, and stops spreading false narratives related to Taiwan," Zhang added.
He also asked Washington to "work with China to promote communication and exchanges between the two militaries and jointly shoulder the responsibilities of major powers".
- 'Avoid miscalculation' -
China has kept up its sabre-rattling since the inauguration this year of President Lai Ching-te, whose party emphasises Taiwan's separate identity.
Thursday's talks also saw Sullivan express "concerns about (Chinese) support for Russia's defense industrial base", the readout added -- echoing longstanding US claims that Beijing has rejected.
He also raised "the need to avoid miscalculation and escalation in cyber space, and ongoing efforts to reach a ceasefire and hostage deal in Gaza", the White House said.
Sullivan's visit comes months ahead of US elections in November.
If she wins, Harris would be expected to continue Biden's approach of seeking dialogue with China while also maintaining pressure.
Her Republican rival Donald Trump has vowed, at least rhetorically, to take a harder line, with some of his aides seeing a far-reaching global showdown with China.
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