Blatter, who is standing down after the election of a new president on Feb. 26, wrote the message to FIFA's 209 member associations on Friday, a day after Secretary-General Valcke's departure following allegations he was involved in a plan to profit from World Cup ticket sales.
The swift action against Valcke was another major blow for Blatter as questions about corruption during his 17-year reign build.
Frenchman Valcke, Blatter's number two since 2007, was placed on leave just hours after a ticket-dealer and ex-footballer Benny Alon made the allegations about the ticket-selling plan at the 2014 World Cup in Brazil.
"I remain confident that we will also be able to come through this difficult situation together, and thank you for your trust," wrote Blatter.
The 79-year-old Blatter, who has been at the helm of football's governing body since 1998, said that FIFA Deputy Secretary General Markus Kattner would take over "operational matters" for now.
The allegations against Valcke come on top of probes by the U.S. Department of Justice and the Swiss Attorney General's Office into corruption at FIFA after the indictment of 14 senior football officials and sports marketing executives in May.
Valcke "unequivocally" denied the allegations as "fabricated and outrageous" in a statement from his U.S. lawyer Barry Berke.
Earlier on Friday, a U.S. judge in Brooklyn, New York, held a hearing regarding two sports marketing executives named in the U.S. indictment -- Alejandro Burzaco and Aaron Davidson.
Evan Norris, a prosecutor, informed U.S. District Judge Raymond Dearie that Swiss authorities had on Thursday approved the extradition to the United States of another defendant, Eugenio Figueredo, a former FIFA vice president, and said prosecutors were in talks with others arrested in Switzerland about coming voluntarily.
"We're hopeful you'll see additional defendants before your honour in the coming weeks and months," he said.
Norris added that the Justice Department anticipated bringing additional charges, but did not have a firm time frame for doing so.
Jeffrey Webb, former president of CONCACAF, the football confederation for North and Central America and the Caribbean, has been extradited to the United States and in July pleaded not guilty to charges of racketeering conspiracy, wire fraud and money laundering.
(Additional reporting by Nate Raymond in New York; Editing by Stuart Grudgings)
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