US and China presidents' summit takes place amid tensions over state-versus-state hacking and revelations about NSA reaping data from phone and internet accounts of millions

President Barack Obama has brushed aside the outcry over surveillance operations by the US government to tell China's President Xi Jinping he wants a world order where all countries play by the same rules on cybersecurity.

Obama opened a two-day summit at a baking Californian desert estate on Friday evening with a call for closer ties between Beijing and Washington, saying he welcomed China's "peaceful rise" and that both sides must balance competition and cooperation.

Obama singled out cybersecurity, as well as North Korea, climate change and intellectual property rights as areas where the US and China needed to cooperate.

He spoke within hours of striking a defiant stance amid revelations about the extent of the surveillance state in the US – a row that analysts said could weaken his efforts to pressure Xi over Chinese hacking.

Xi made no mention of the issue in opening remarks in which he said the talks were a chance to "chart the future" of bilateral ties. "Relations between our two countries are at a new historical starting point," he said.

Officials on both sides said meeting so soon since Xi's ascent to the presidency in March signalled a desire to build a personal rapport between the two leaders. The Americans chose Sunnylands, a 200-acre estate in Rancho Mirage, as the venue to foster an intimate, relaxed atmosphere in contrast to the stiff formality of White House meetings.

The presidents wore suits but no ties as they posed in gardens with a dramatic mountain background in melting temperatures upwards of 100 degrees (38C).

At preliminary talks before a working dinner, Obama said China's success was in US interests. Despite inevitable "areas of tension" both sides must obey the same rules, he said. "I'm very much looking forward to this being a strong foundation for the kind of new model of co-operation that we can establish for years to come."

Obama was expected to push cybersecurity again on Saturday despite the awkward timing of revelations by the Guardian and the Washington Post that the National Security Agency uses companies such as Google, Facebook and Apple to obtain information that includes the content of emails and online files. The admission that authorities had undertaken a seven-year programme to monitor the telephone calls of potentially millions of people in the US shows the Obama administration has embraced and expanded a surveillance regime begun under George Bush.

Xi Jinping and Barack Obama at their summit in California. Photograph: Evan Vucci/AP

Obama tried to take the sting out of the issue in a visit to Silicon Valley earlier on Friday when he defended the surveillance as a "modest encroachment" on privacy needed to protect the US from terrorist attack. "You can't have 100% security and then also have 100% privacy and zero inconvenience. We're going to have to make some choices as a society."

The Chinese deny digitally pillaging US corporate secrets and say they have been victims of such attacks. Fresh revelations in the Guardian that the White House ordered officials to draw up overseas targets for hacking may complicate Obama's bargaining.

Xi, who is considered more open and comfortable in public than his dour predecessor, Hu Jintao, arrived in the US after visiting Latin America and the Caribbean.

He said that in the past four decades China-US relations had gone through "wind and rain" and reaped huge benefits from co-operation. "When I visited the United States last year I stated that the vast Pacific Ocean has enough space for the two large countries of China and the United States. I still believe so."

China's president is expected to lobby his host over alleged discrimination against Chinese firms in US markets. Another complaint is the expanding US military presence as part of Washington's "pivot" to the Asia-Pacific region.

The table for the working dinner was set with eight chairs on each side, each with fine china, a water glass and two wine glasses.

In a sign of sensitivities some Chinese commentators interpreted Michelle Obama's absence from the summit as a snub to Xi's wife, Peng Liyuan. China's first lady visited the nearby Palm Springs art museum with Anne Gust Brown, the wife of California's governor, Jerry Brown.

Police kept several hundred anti-Beijing protestors on a stretch of Bob Hope Drive outside the walled Sunnylands estate.

Representatives of the Falun Gong spiritual sect, which China has banned as a cult, said they wished to highlight abuses. "We are being persecuted and tortured to death. We want this to stop," said Maggie Wu, who travelled from San Francisco.

Vietnamese exiles who fled their homeland in the 1970s held banners accusing Beijing of controlling the country's communist rulers. "We lost our country to red China. They took our homes, our land, everything," said Marie Nguyen, 73, from Torrance, near Los Angeles.