Tillerson said Trump and Xi had "extensive discussions around the unsafe situation in North Korea" during their meeting at Mar-a-Lago last week.
"President Xi ... shared the view that this has reached a very serious stage in terms of the advancement of North Korea's nuclear capabilities", Tillerson said.
China is North Korea's main diplomatic and economic ally. "We feel the increased presence is necessary", the official said.
"China will either decide to help us with North Korea or they won't".
The move infuriated Beijing, leading Trump to eventually reiterate his commitment to the decades-old policy.
President Donald Trump proclaimed the success of his summit with China on Saturday, tweeting, "It was a great honor to have President Xi Jinping and Madame Peng Liyuan of China as our guests in the United States".
"The US missile attack against Syria is a clear and unforgivable act of aggression against a sovereign state and we strongly condemn this", KCNA quoted an unnamed spokesman for the North Korean foreign ministry as saying.
Sitting with Mr. Trump during a major national security incident gave the Chinese leader an "unprecedented" opportunity to view at close range how the USA leader, less than 100 days into his presidency, acts under pressure, John Park, a specialist on Northeast Asia at Harvard Kennedy School, said in a telephone interview.
Tensions are running high around the Korean Peninsula amid speculation that the North might carry out an additional nuclear test or a long-range missile launch this month filled with big events, which Pyongyang has often celebrated with a show of military force.
The leaked proposals could be aimed at persuading Xi into pressuring North Korea - its ally and trade partner - to face the music and come back to the table over its nuclear weapons program, former US ambassador to South Korea Kathleen Stephens told the Herald.
"China is willing to work with the worldwide community to promote a political settlement for the Syrian issue at an early date", Hua said.
China-which supplies 90 percent of North Korea's food and energy-could force Kim Jong-un to the negotiating table.
"Armed with nuclear weapons, he would hardly flinch at the attack in Syria", Chang said.
On a question about whether a pre-emptive USA strike on the North will be in breach of the 1973 Armistice Agreement, the official said he would not talk about a "hypothetical" matter. It claims its nuclear weapons are a necessary deterrent to the US military threat.
On Saturday evening, the White House also released a readout of President Trump's call to Saudi King Salman bin Abd al-Aziz Al Saud who reaffirmed strong Saudi support for the United States military strike against the Sayrat Airfield on Friday and thanked Mr Trump "for his courageous action". The relationship developed by President Xi and myself I think is outstanding.
"The Syria attack thoroughly reminds us the fact that it is absolutely unsafe to have any illusions about imperialism and only military power of our own will protect us from imperialistic aggression", he added.
In between the summit and the party congress, Chinese leaders would want to keep the Sino-US relationship on a positive track, for which they would be willing to make compromises, according to Pang Zhongying, a professor of worldwide relations at Renmin University.
A statement from Syria's general military command said the strikes caused "extensive material damage" and undermined counterterror operations by the Syrian army.