Discussions on trade and North Korea appear to have dominated the just-completed talks held at Trump's Mar-a-Lago resort in Florida.
"I believe lots of very potentially bad problems will be going away", Trump predicted.
Noting that the two leaders had positive and productive meetings, Spicer said Trump and Xi agreed to work in concert to expand areas of cooperation while managing differences based on mutual respect.
The leaders met amid a host of thorny issues, including regional maritime disputes, Chinese base building in disputed islands, and the recent deployment of a USA air defense system to South Korea that Beijing fears could be used for espionage. Trump was meeting again with his Chinese counterpart Friday, with US missile strikes on Syr.
Confronting his first foreign policy crisis, Trump relied largely on seasoned military officers - Mattis, a former Marine general, and McMaster, a U.S. Army lieutenant general - rather than the political operatives who had dominated his policy decisions in the first weeks of his presidency, said three officials involved in the deliberations.
The actions against the government of Syrian President Bashar Assad in response to a chemical attack come in spite of the prospect of escalating Russian ill will that could further inflame one of the world's most vexing conflicts.
Patrick Cronin, a China expert with the Center for a New American Security, said the Trump administration does not have "a reconciled trade and economic policy yet, and the differing views on China in the White House underscore that".
Earlier this month President Trump sent an unmistakable message to China about North Korea, without a metaphor.
Trump had promised during the campaign to stop what he called the theft of American jobs by China.
Afterward, Xi and other Chinese leaders seemed hesitant to respond to the missile strike, a military intervention they would usually oppose - China repeatedly has used its veto power to block U.N. Security Council resolutions on Syria, including a 2016 plan for a cease-fire in Aleppo and proposed sanctions on the use of chemical weapons.
After the meeting, Trump took Xi on a walk around the manicured grounds of his lavish Spanish-style complex.
On North Korea, Tillerson says that while Trump and Xi's discussions on North Korea were very "wide-ranging", and "focused entirely on both countries' previous commitments to denuclearize the peninsula", there was "no kind of a package arrangement discussed to resolve this". Chinese state media reported late Thursday that Trump has accepted Xi's invitation to visit China this year.
Ross noted a new 100-day plan for trade discussions between the USA and China.
Trump and Xi are spending part of Friday in talks at Trump's estate in Florida.
Trump and Xi agreed to increase cooperation and work with the worldwide community to convince North Korea to peacefully resolve the issue and dismantle its illegal nuclear and missile programmes, he said, adding that the two sides had a candid discussion on regional and maritime security.
Disagreements over approaches to North Korea or bilateral trade could, if mishandled, destabilize North East Asia or tank the global economy.
China has not directly said it is targeting South Korean companies.
President Donald Trump says it's been "very interesting" to spend time with Chinese President Xi Jinping and his delegation.