Updated 9:21 PM ET
RANCHO MIRAGE, Calif. President Obama is said to have laid it on the line to President Xi Jinping about computer hacking emanating from China and targeting the U.S.: shut it down or face the a less productive relationship.
But White House National Security Advisor Tom Donilon described the U.S.' hard line in more diplomatic terms.
He said Mr. Obama made it clear to Xi Jinping that if the "cyber-enabled economic theft" by "entities" in China does not end, it would be a very difficult problem in the economic relationship and "an inhibitor" to other progress between the U.S. and China.
Donilon said the hacking is more than just unpleasant cyber intrusions against the U.S. He said it's "inconsistent with the kind of relationship we want to build with China."
"We're talking about an entity in China engaged in the theft of public and private intellectual property." Donilon said Mr. Obama asked Mr. Xi to seriously address the issue.
Mr. Xi said Friday that his country is also a victim of cyber attacks.
The two leaders dined Friday night on a meal prepared by chef Bobby Flay: lobster tamales, Porterhouse steak and "classic" cherry pie,
The issue menu focused on North Korea.
The leaders engaged in what was described as "lengthy discussion" about North Korea, which the U.S. and most of the world views as a rogue state. The White House continues to hope that China can use its influence to get North Korea's unpredictable and erratic leader Kim Jong Un, to abandon his government's production of nuclear weapons and long-range missiles and stop its provocative actions against South Korea.
Donilon said China has taken steps to send a clear message to North Korea. He said there was agreement between Presidents Obama and Xi that this was "a clear area for cooperation."
They had quite a good discussion about it, said Donilon, and agreed to work together.
The two leaders began their second and final day of talks with a gentle Saturday morning stroll around some on the idyllic grounds of Sunnylands, a lush and verdant 200-acre estate in this desert resort community.
The two leaders were dressed casually in open collar and shirt sleeves: Mr. Obama had his sleeves rolled up, Mr. Xi's were buttoned down. No suit jackets like yesterday. No ties either.
"Terrific," said Mr. Obama, responding to a reporter asking how the talks were going.
According to Donilon, the leaders met for a total of eight hours over two days. He called the sessions "quite unique and important."
The estate, alternately opulent and rustic, lavish and down-home, was built in the mid-1960s for billionaire publisher and philanthropist Walter Annenberg and his wife Lenore.
The White House felt the venue provided just the right kind of informal atmosphere in which the two leaders could get acquainted and discuss such contentious issues as breaches of cybersecurity.
The temperature was already near 90 degrees at 9:15 in the morning as the leaders took their walk. They came to rest on a bench strategically positioned for them to sit upon. Custom-designed and made of California Redwood, the bench was a gift from Mr. Obama to his Chinese guest.
The bench carried an inscription in English and Mandarin:
"Presented to his Excellency Xi Jinping President of the People's Republic of China by Barack Obama President of the United States. Sunnylands Annenberg Estate. June 7-8, 2013."
It ruffled some feathers in China that first lady Michelle Obama did not accompany her husband to the summit although Mr. Xi's spouse, Peng Liyuan, did."
After the summit ended, a White House official said Mrs. Obama had sent Madame Peng a note, welcoming her to the U.S. and expressing regret for missing the summit. Mrs. Obama said she hoped to have the chance to visit China soon and meet her counterpart there.
Part of the leaders' walk around Sunnylands took them onto the Annenberg golf course, but they did not play. The temperature hit 114 degrees Friday and was headed almost as high on day two of their summit.
Nevertheless, after the summit ended, the White House let it be known that Mr. Obama hit the links with three of his pals from Hawaii -- despite the 103-degree heat.
Mr. Xi made it clear he found the Sunnylands venue amenable and repeated his hope that the summit would help lay the groundwork for building "a new model of major country relationship" between the U.S. and China.
"When the U.S. and China work together," said Mr. Xi on Friday, "we can be an anchor of world stability and a propeller of world peace."
He spoke of deepening understanding and trust between the two countries in order to avoid "inevitable confrontations" and embark on a new path.
Mr. Obama seconded that objective. He said more could be accomplished if the U.S. and China worked cooperatively rather than in conflict.
Mr. Xi has invited Mr. Obama to visit China for a reciprocal summit, but no date has yet been set.