The american president, who had violently criticized China during his election campaign, has also "reiterated its determination to get trade more balanced with the commercial partners of the United States", according to the same source.
China hopes that the US will handle the Taiwan issue appropriately in accordance with the "One China" principle and the three China-US joint communiques, Xi said.
Ruggiero said the decision to sanction Dandong was "long overdue", adding pressure could be put on China through their need for United States currency.
"Xi stressed that both China and the United States need to control the general direction of the bilateral relationship in light of the consensus reached at the Mar-a-Lago summit", China's government said.
China's foreign ministry accused the U.S. of violating Chinese sovereignty and disrupting "peace, security and order of the relevant waters" after the U.S. Navy destroyer USS Stethem sailed Sunday within 12 nautical miles (22 kilometers) of tiny Triton island, which is claimed by China, Taiwan and Vietnam. But he and his Chinese counterpart still spoke on Monday about North Korea.
Editor's Remarks: The recent US-China Dialogue meeting in Washington does not seem to have gone well and talks between the US and Chinese Presidents at the G20 summit this week could turn frosty.
Obama said North Korea's future prosperity would not come "from the pursuit of nuclear weapons". He pronounced his intention to cooperate with Japan and South Korea to increase pressure on North Korea by enforcing sanctions.
Cheng Xiaohe, an associate professor of global relations at Renmin University in Beijing, said that given the recent actions by Mr Trump, it was "a little bit odd" that Mr Xi had agreed to the phone call.
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U.S. blacklists China bank, revving up pressure over NKorea
The sanctions freeze any assets of these individuals on american soil and forbidden to have commercial relations with them. As such, he is considering possible trade actions against Beijing, three senior administration officials said.
Over the past week, though, the US has taken aim at China on numerous issues: downgrading China to its lowest Tier 3 regarding its efforts to combat human-trafficking; robustly criticizing Beijing over its treatment of jailed dissident and Nobel Peace Prize victor Liu Xiaobo, who is suffering from terminal cancer; agreeing $1.4 billion of American arms sale to Taiwan; and imposing secondary sanctions on Chinese firms doing business with North Korea.
The President even agreed a $1.3billion arms sale in Taiwan, which is viewed as a renegade province of China.
However, analysts have claimed Mr Trump is being put off the relationship by China's failure to reign in neighbouring dictator Kim Jong-Un.
The U.S. Department of the Treasury placed sanctions on China's bank of Dandong due to suspicions of illicit transactions with North Korea.
Trump issued a statement on Warmbier's death: "There is nothing more tragic for a parent than to lose a child in the prime of life".
Beijing was also irritated after the USA state department gave Beijing a dismal grade last week in a new human trafficking report.
"I don't see that alone as a provocation towards China, rather I think if we connect up these other areas, including sanctions on Chinese entities, that's the thing to watch". Today China has landing craft, advanced fighters, ships and submarines.
The agreement, which was always likely to have gone ahead, appeared to have been at least temporarily shelved, as Trump looked to build closer ties with China.