Danish newspaper BT had originally reported that Riis had been suspended over recent poor results, leading to a storm of speculation that the 1996 Tour de France winner was to be replaced as team boss.
"Following the rumours and speculations published by many Danish media first and then by international cycling media later last night, Tinkoff Saxo would like to clarify that Bjarne Riis is not being actively involved in the team's activities since last Sunday," the statement said.
"However, he was not suspended of his active role because of lack of results nor for financial issues. The team management has full confidence in the technical and performance team, in all the riders and staff members and is currently working to establish the best way forward in the racing season.
"No decisions have been taken and any formal and final decision on any team member, if taken, shall be communicated at the appropriate time. Until then there will be no further comments on this matter."
Sources within the team claim the club's controversial Russian owner Oleg Tinkov blames the 50-year-old Dane for poor results so far this season.
Team leader Alberto Contador spoke out in support of his team chief, although he said he was in the dark over the suspension.
"Right now the first thing is to truly understand the situation because all we know is what is in the statement and basically we need to know why this decision has been taken," he said before the start of Tuesday's second stage of the Volta a Catalunya.
And he added that Riis is "someone very important in my career".
Riis won the 1996 Tour de France, but admitted in 2007 that he used EPO (erythropoietin) to secure victory, although his win has not been officially erased from the race's record books.
Riis was in partnership with Tinkoff Credit Systems ahead of the 2013 season, and the following year sold the team, which he has run since his retirement in 1999, to Tinkov.