* Obama says up to Mexico to determine own security structure
* Obama, Pena Nieto seek to spotlight business, trade ties
* Presidents agree to push Asia-Pacific trade deal
* Cross-border oil drilling deal also discussed
MEXICO CITY, May 2 (Reuters) - U.S. President Barack Obama gave his blessing on Thursday to a new security arrangement with Mexican leader Enrique Pena Nieto, in which Mexico will make reducing violence a priority over hunting drug cartel kingpins in the war against organized crime.
The two presidents said they also want to step up trade and business ties that have been overshadowed by the battle against drug trafficking.
"It is obviously up to the Mexican people to determine their security structures and how it engages with other nations including the United States," Obama said at a joint press conference with Pena Nieto.
At the start of a two-day visit to Mexico, Obama sought to draw attention to the emerging might of Latin America's No.2 economy, even as worries about containing drug-trafficking and related violence remained an inescapable subtext.
The two leaders pledged to begin holding cabinet level meetings focused on boosting business between the two countries and to expand educational changes. The first high-level meeting is set for the fall.
The U.S. president pledged support for Pena Nieto's new policy of restricting contacts with the United States on drugs and drug-related violence to a single point, Mexico's Ministry of the Interior. He acknowledged that the United States can play a role with its own domestic policies.
"We look forward to continuing our good cooperation in any way," he said. "I also reaffirmed our determination in the United States to meet our responsibilities to reduce the demand for illegal drugs and to combat the southbound flow of illegal guns and cash."
Mexico's new "single-door" policy would be an abrupt change from the wide latitude the U.S. government enjoyed in working with Mexican officials across agencies under Pena Nieto's predecessor, Felipe Calderon.
The change has raised questions about Mexico's commitment to combating drug trafficking and drug-related violence.
Pena Nieto plans to shift the weight of combating organized crime from the military onto a new militarized police force, but has made few concrete changes so far, instead seeking to focus public attention on the economy rather than violence.
The Mexican government has said that killings linked to organized crime fell 14 percent in the first four months of Pena Nieto's presidency, but 4,249 people still were killed during that period.
More than 70,000 people are estimated to have been killed in drug violence in Mexico since 2007, and gang-style murders continue to provide lurid headlines.
Some question whether Calderon's aggressive policies, which focused on eradicating gang leaders, has been successful or whether it has generated additional violence as rival factions vie for control of turf.
Pena Nieto said his approach will emphasize reducing bloodshed and will operate more smoothly.
"Under this new strategy, what we are trying to do is put in order, institutionalize the security cooperation we have today with the United States, and establish clear and singular channels to help us be more efficient and achieve better results," Pena Nieto said in Spanish.
In a letter to Obama ahead of his visit, rights group Human Rights Watch urged him to review the United States' public security approach with Mexico, rapping his administration for offering "uncritical support" for Calderon's policies and citing a "dramatic increase" in rights abuses.
Both Obama and Pena Nieto have said they want the visit to focus on economic issues rather than security. Pena Nieto is eager to underscore Mexico's recent run of solid economic growth, fueled in part by its increasing attractiveness as a manufacturing hub.
The leaders pledged to conclude a trade agreement with Asia-Pacific nations, the Trans-Pacific Partnership, by the end of the year.
By highlighting Mexico's progress in moving up the economic ladder, Obama is also emphasizing that his own domestic goal of reforming U.S. immigration laws will not promote an exodus of Mexicans into the United States.
"Part of what we discussed is the importance of getting it done, precisely because we do so much business between our two countries," he said, referring to immigration reform that has drawn bipartisan support in Washington. "If we're going to get that done, now's the time to do it."
The two presidents at their meeting discussed a much publicized energy agreement that would remove obstacles to expanding deepwater drilling for oil in the Gulf of Mexico. They said in a joint statement that they looked forward to implementation of the deal.
The United States has yet to finalize the deal, known as the Transboundary Hydrocarbons Agreement, which provides guidelines for drilling in an area of the Gulf that straddles the U.S.-Mexican boundary.
The deal is seen as the key to opening a new era of cooperation on oil production between the two countries. Mexico's state-owned oil company Pemex needs technology and investment to boost its stagnant production, and U.S. companies are eager to help.