He said that the organization had set up 486 centers for receiving aid across Mexico's 32 states and that the state-run Family Integration Directorate was also receiving donations in central state Hidalgo.
"Our goal is to send as much aid as we receive every day, but for the moment all that has been donated is held in warehouses," Cardenas told Mexican broadcasters.
Earlier on Thursday, The Mexican Red Cross officials said that an aircraft with one ton of Red Cross aid, and one ton contributed by the Mexican police, had left a military air base for Port-au-Prince, capital of Haiti.
He called for Mexicans to donate tinned food, bottled water and medicines, as being the most important. He also called for plates, drinking vessels, toilet paper, tampons, pasta and toothbrushes.
Haiti suffered an earthquake measuring 7 on the Richter scale on Tuesday, which struck on shore, just 25 kilometers from the nation's capital Port-au-Prince. Haitian President Rene Preval estimated that as many as 50,000 people may have died in the quake.