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Mexico City • President Barack Obama sought on Thursday to tamp down a potential rift with Mexico over a dramatic shift in the cross-border fight against drug trafficking and organized crime, acceding that Mexicans had the right to determine how best to tackle the violence that has plagued their country.

Since taking office in December, Mexican President Enrique Pena Nieto has moved to end the widespread access that U.S. security agencies have had in Mexico to tackle the violence that affects both sides of the border. It's a departure from the strategy employed by his predecessor, Felipe Calderon, which was praised by the U.S. but reviled by many Mexicans.

Obama said the shifting security relationship would not hurt cooperation between the neighboring nations.

"I agreed to continue our close cooperation on security, even as the nature of that cooperation will evolve," Obama said during a joint news conference at Mexico's grand National Palace. "It is obviously up to the Mexican people to determine their security structures and how it engages with the other nations — including the United States."

Pena Nieto as well downplayed the notion that the new, more centralized arrangement would damage its security partnership with the United States. He said Obama agreed during their private meeting earlier in the day to "cooperate on the basis of mutual respect" to promote an efficient and effective strategy.

Obama arrived in Mexico Thursday afternoon for a three-day trip that will also include a stop in Costa Rica. Domestic issues followed the president south of the border, with Obama facing questions in his exchange with reporters about the potential escalation of the U.S. role in Syria, a controversy over contraception access for teenage girls, and the delicate debate on Capitol Hill on an immigration overhaul.

The latter issue is being closely watched in Mexico, given the large number of Mexicans who have emigrated to the U.S. both legally and illegally. More than half of the 11 million people in the U.S. illegally are Mexican, according to the Pew Research Center.

For Obama, the immigration debate is rife with potential political pitfalls. While he views an overhaul of the nation's patchwork immigration laws as a legacy-building issue, he's been forced to keep a low-profile role in the debate to avoid scaring off wary Republicans.

In an effort to court those GOP lawmakers, the draft bill being debated on Capitol Hill focuses heavily on securing the border with Mexico, and makes doing so a pre-condition for a pathway to citizenship for those in the U.S. illegally. But Florida Republican Sen. Marco Rubio, one of the bill's architects, said Thursday that unless the border security measures are made even tougher, the legislation will face tough odds not only in the GOP-controlled House but also in the Democratic-led Senate.

The president acknowledged there were some areas along the 2,000-mile border between the U.S. and Mexico where security needs to be tightened. But he gently chided Rubio and other Republicans for putting up obstacles that would derail final legislation.

"I suspect that the final legislation will not contain everything I want. It won't contain everything that Republican leaders want, either," Obama said. He added that "what I'm not going to do is to go along with something where we're looking for an excuse not to do it as opposed to a way to do it."

Despite the intense interest in the immigration debate among Mexicans, Pena Nieto carefully avoided injecting himself in the issue. While he commended the U.S. for tackling the challenge, he said the congressional debate "is a domestic affair."

The new Mexican leader was purposely seeking to avoid the perceived missteps of former Mexican President Vicente Fox, who irked conservatives in the U.S. by lobbying for an immigration overhaul in 2001.

Pena Nieto's election brought Mexico's Institutional Revolutionary Party, or PRI, back to power after a decade on the sidelines. The security changes are emblematic of the party's preference for centralized political and bureaucratic control.

The arrangement means all contact for U.S. law enforcement will now go through a "single door," according to Mexico's federal Interior Ministry, the agency that controls security and domestic policy. Under the previous policy, FBI, CIA, DEA and border patrol agents had direct access to units of Mexico's Federal Police, army and navy. U.S. agents worked side by side with those Mexican units in the fight against drug cartels, including the U.S.-backed strategy of killing or arresting top kingpins.

Obama lauded his Mexican counterpart for launching bold reforms during his first months in office, not only on security but also the economy. Both leaders have said they want to refocus the U.S.-Mexico relationship on trade and the economy, not the drug wars and immigration issues that have dominated the partnership in recent years.

In a nod to that effort, Obama and Pena Nieto announced a new partnership for closer cooperation between top officials in both countries. Vice President Joe Biden will also participate in that process, Obama said.

Already the economic relationship between the two countries is robust, with Mexico accounting for $500 billion in U.S. trade in 2011 and ranking as the second-largest export market for U.S. goods. A stronger Mexican economy would result in even more trade and job growth on both sides of the border, Obama aides say.

On Friday, Obama will speak to an audience of Mexican students before heading to Costa Rica for talks with Central American leaders. His meetings there are expected to focus on bolstering regional economic cooperation, as well as security issues. Rubio seeks stronger tack on border security

Washington • Sen. Marco Rubio says a new immigration bill he helped write needs stronger border security provisions or it will fail in the House and may even struggle to pass the Senate. The Florida Republican is the chief emissary to conservatives on the contentious legislation. He says he's been hearing concerns in recent days that more work is needed to boost the bill's language about the border. He says he's committed to trying to make those changes. Rubio didn't give specifics in an radio interview. But a number of conservatives have complained about "triggers" in the bill that aim to make new citizenship provisions contingent on border security accomplishments. Critics say those provisions are too weak.