* Reform will be discussed more widely with financial institutions * Delay powered peso rally * U.S. warned Bank of Mexico reform could endanger bilateral transactions (Adds comment from official, details) MEXICO CITY, Dec 15 (Reuters) - Mexican lawmakers on Tuesday agreed to overhaul a new central bank bill that shook confidence in the country’s financial system, and which authorities warned could force the bank to add laundered drug money to its reserves. In a move that boosted the peso currency, the lower house of Congress put the brakes on the bill’s approval process after critics ranging from the Bank of Mexico (Banxico) to the United States, ratings agencies and even members of the government said it could undermine Mexico’s financial credibility. “As was just made public, lawmakers postponed discussion of the Banxico law. It seems to us they have taken the appropriate measure by allowing space for a more technical and in-depth discussion,” Finance Minister Arturo Herrera said on Twitter. The peso strengthened more than 1.5%, having gained over 0.5% after Reuters reported the postponement, breaking the psychological 20 pesos-per-dollar barrier to firm to below 19.9 per dollar. Mexico’s currency posted four consecutive days of losses prior to Tuesday as investors eyed the legislation nervously. “There is no doubt that the depreciation the peso had accumulated during the week was largely due to a greater perception of risk in Mexico,” said Gabriela Siller, an economist at bank Banco Base. The bill will be now be reviewed by a panel made up of the two houses of Congress, the central bank, finance ministry and regulators, with the aim of reaching consensus in January, Senate majority leader Ricardo Monreal said at a media conference with his lower house counterpart Ignacio Mier. Banxico said it was willing to continue working with Congress, while insisting its autonomy be respected. The reform pitched by Monreal proposed making Banxico buy up foreign cash, which banks cannot repatriate. Supporters said it would help migrants and hospitality workers exchange dollars. Nevertheless, the Senate’s approval of the law last week prompted a stern rebuke from Banxico, business groups, banks and economists, all fearful that it could allow money from drug cartels to enter the bank’s international reserves. In business, billionaire Ricardo Salinas, who controls lender Banco Azteca, stood out in his support for the law. One member of Banxico’s board suggested he was the bill’s main beneficiary. President Andres Manuel Lopez Obrador, who sets great store by peso stability, helped underline to lawmakers the need to rework the legislation, an official said. Some U.S. authorities tasked with policing illicit operations expressed concern the bill could hamper international operations between U.S. banks and their Mexican peers and Banxico, Banxico Governor Alejandro Diaz de Leon said last week. The bill could jeopardize accords between Banxico and foreign financial authorities, and violate bilateral relations between Mexico and other countries, particularly the United States, Diaz de Leon told lawmakers on Friday, pointing to a dollar swap line the U.S. Federal Reserve has with Mexico. Officials in the U.S. Treasury Department and the Fed had expressed concerns to Mexico about the bill, according to a person familiar with the matter. Neither U.S. institution responded to requests for comment. Banxico has relied on transactions with the Fed to help stabilize the peso and access dollars when demand surges during crises, such as at the outset of the coronavirus pandemic. It was one of nine central banks granted access to the Fed’s U.S. dollar liquidity swap lines in March, and it has tapped into them, with a peak draw of nearly $6.6 billion. While that balance has dropped, the bank has kept the lines open and has rolled over more than $1 billion in the past week.