President Obama moved quickly Saturday to project the image of renewed American leadership in the Asian Pacific, announcing broad agreement on a multi-nation free-trade pact and warning China that it must “play by the rules” as its international influence increases.

On the first day of the Asia-Pacific Economic Cooperation summit here, Obama sketched out his administration’s vision of an expanded U.S. role, telling a ballroom of hundreds of business leaders that the newfound engagement is a “reaffirmation of how important we consider this region.”

“On the business side, this is where the action’s going to be,” Obama said. Later, he added, “I’m very proud of the leadership America has shown in the past, but I also don’t want to underestimate the leadership we’re showing now.”

Yet even as Obama sought to establish U.S. primacy, his Chinese counterpart, President Hu Jintao, offered a competing vision for regional growth — one with dynamic Chinese markets and improving internal business standards as the driving engine.

“China has huge market potential and capital,” Hu told the same business leaders. “China will work hard to turn itself into an innovation-driven country . . . so we can transition from ‘made in China’ to ‘created in China.’ ”

Their comments came hours before the two presidents held a bilateral meeting, at which Obama stressed that cooperation between the two powers was “vital to the world.”

Although Hu said he was confident the countries could work constructively based on “mutual respect and mutual interest,” reporters allowed into the room for the opening remarks noticed that the Chinese leader did not look at Obama while either spoke.

After the meeting, Michael Froman, a U.S. deputy national security adviser, told reporters that the president was clear with Hu that the American business community is “growing increasingly impatient and frustrated with the state of change in China economic policy and the evolution of the U.S.-China economic relationship.”

Froman added that Hu “heard the message and understood the implications of it.”

The early political maneuvering set the tone for what is expected to be ongoing competition for influence with China during Obama’s nine-day trip through the Asia Pacific, which includes stops in Australia, to announce a new military partnership, and Bali, Indonesia, for a regional security summit.

Early Saturday, Obama hailed progress on the Trans-Pacific Partnership, a free trade agreement with eight other nations that his administration has said will help create jobs as it opens foreign markets to U.S. exports.

He said the United States and other countries — Brunei, Chile, New Zealand, Singapore, Australia, Malaysia, Peru and Vietnam — reached broad agreement on the pact and are aiming to have legal language for the framework in place by next year. Japan, which has announced its intention to start discussions on joining the partnership, was not involved in Saturday’s meeting.

“With nearly 500 million consumers between us, there is so much more we can do together,” Obama said.

Even with that pact, however, there was friction with China, which has the world’s second-largest economy. Chinese officials complained that they were not invited to the talks, but Froman said the agreement is “not something that one gets invited to. It’s something that one aspires to.”

In Obama’s appearance before the business leaders, the president, who fielded questions from Boeing chief executive W. James McNerney Jr., said there can exist a “friendly and constructive competition” with China. But Obama emphasized that the Chinese must be willing to revalue their currency rates to balance trade, respect intellectual-property rights and allow U.S. companies to compete fairly for contracts inside China.

“The bottom line is the United States cannot be expected to stand by if there is not reciprocity in trade and economic relations. We will continue to bring it up,” Obama said. “There is no reason why this should inevitably lead to sharp conflict. There’s a win-win opportunity there. In the meantime, where we see rules broken, we’ll continue to speak out and bring action.”

While chiding China, Obama also reserved a gentle rebuke for his own nation, saying the United States had become a “little bit lazy” in the past couple of decades in the global marketplace.

“We’ve kind of taken for granted — well, people will want to come here and we aren’t out there hungry, selling America and trying to attract new business into America,” Obama said.

For his part, Hu painted the picture of a central government actively engaged in creating a more open and transparent business environment where international companies can invest with the comfort that they will be treated fairly.

He acknowledged that China lacks innovation and that its well-developed urban areas and slower-paced rural economies “lack coordination.” And he pledged stronger government action to crack down on intellectual property rights violations.

But, he stressed, “China’s development constitutes an important force driving economic growth in the Asia Pacific region and the world.”