MEXICO CITY, Oct 8 (Reuters) - U.S. Secretary of State Antony Blinken on a visit to Mexico on Friday held talks with President Andres Manuel Lopez Obrador, with both nations vowing to revitalize fractious relations and improve cooperation through a major new security agreement. The top U.S. diplomat visits Mexico at a time when the Biden administration is increasingly reliant on its southern neighbor to stem the flow of Latin American migrants heading to the United States. Blinken"s visit is part of the Biden administration"s first U.S.-Mexico High-Level Security Dialogue, in which the two countries will negotiate a sweeping new agreement on how to tackle everything from drug flows to the United States to the smuggling of U.S.-made guns into Mexico. Overhauling the Merida Initiative accord, under which the United States channeled about $3.3 billion since 2007 to help Mexico fight crime, is expected to take many months as the two sides work out how best to work together following a period of strained cooperation"After 13 years of the Merida Initiative, it"s time for a comprehensive new approach to our security cooperation, one that will see us as equal partners in defining our shared priorities," Blinken said. Earlier, Lopez Obrador took Blinken on a tour of the murals at the National Palace before the two delegations had a working breakfast. The Mexican leader said in a tweet afterward that there were "excellent conditions to inaugurate a new stage of the bilateral relationship." He also invited U.S. President Joe Biden to visit. U.S. Secretary of Homeland Security Alejandro Mayorkas and U.S. Attorney General Merrick Garland accompanied Blinken, who also met with Foreign Minister Marcelo Ebrard. U.S.-Mexico relations suffered a major blow last October when U.S. anti-narcotics agents arrested Mexican former defense minister Salvador Cienfuegos, outraging the Mexican government. Cienfuegos was freed amid intense Mexican pressure, but the detention strained relations and hurt security cooperation.U.S. officials are touting the new security accord as broader than the Merida Initiative, which initially provided military equipment for Mexico and later helped train Mexico"s security forces, police and the judiciary. Lopez Obrador has been a vocal critic of the program, saying it was tainted by its association with previous governments and its failure to prevent bloodshed and escalating violence in the so-called war on drugs. Mexican officials say the new agreement will likely focus on the exchange of information, the root causes of violence, and stemming the flow of U.S.-made guns to Mexico, a key point of concern for Lopez Obrador. read more But negotiating a new agreement will be painful. The United States wants a more muscular approach to battling drug cartels while Lopez Obrador prefers softer and less confrontational methods to fighting gangs, said Vanda Felbab-Brown, a security and foreign policy analyst."There is a minimal area of overlap," said Felbab-Brown, a senior fellow in the Foreign Policy program at the Brookings Institution, a Washington think tank. "The U.S. is in an awkward position here because the Lopez Obrador administration is very comfortable with ending security cooperation." What is more, the talks about the new security cooperation may be overshadowed by immigration concerns. A surge in the number of Haitian and other Latin American migrants arriving at the U.S.-Mexico border plunged the Biden administration into another crisis last month and underlined Washington"s reliance on Mexico to help stem the flow. Mexico"s importance in managing immigration has given the Lopez Obrador administration leverage to pursue more independent policies in other areas, Mexican officials say privately. During the U.S. presidential transition early this year, Mexico made it tougher for American law enforcement agents to operate in the country. Mexico has also delayed visas for U.S. anti-narcotics officers, the U.S. media has reported. A senior Mexican security official said there was optimism about the new agreement on the Mexican side and there may be scope to review the restrictions imposed on U.S. agents operating on Mexican soil, but the conditions cannot return to how they were before Cienfuegos" arrest. "I think part of the U.S. government knows that that"s not possible," the Mexican official said.