WASHINGTON — Congressional Republicans said Monday that they would open an investigation into undercover operations by the Drug Enforcement Administration in which agents have laundered and smuggled millions of dollars in drug money as part of an effort to help Mexico fight organized crime.

The operations, which drug officials said had the support and cooperation of the Mexican government, have funneled hundreds of thousands of dollars across borders and moved millions more through shell accounts to help American agents identify how criminal organizations move their money, where they keep their assets and who their leaders are.

Critics said the operations blur the line between surveillance and facilitating crime, raising questions similar to those around a gun-smuggling operation known as Fast and Furious that involves agents of the Bureau of Alcohol, Tobacco, Firearms and Explosives.

The gun operation has been under investigation for months by Representative Darrell Issa, chairman of the House Oversight and Government Reform Committee. In a letter on Monday to Attorney General Eric H. Holder Jr., Mr. Issa said he would expand that investigation to include the drug agency, describing its money-laundering investigations as “dangerous schemes” and adding that “the consequences have been disastrous.”