A board meeting was held on Thursday amid claims that chief executive Gordon McKie has been under pressure from members over the direction of Scottish rugby.
Glasgow and Edinburgh both finished in the bottom half of the Magners League last season, while Scotland only avoided the Six Nations wooden spoon courtesy of points difference.
However, the SRU insisted there was unity among the 11 board members.
An official statement read: "Following today's meeting of the Scottish Rugby Board, the board unanimously reaffirmed its support for and confidence in Scottish Rugby's established and successful system of governance.
"The board is committed to ensuring this well established system is maintained going forward.
"This system clearly defines the roles and responsibilities of the executives, non executives (including chairman) and council members of the board, as well as the relationship between the board and the Scottish Rugby Council.
"Each of these groups has an important but different set of responsibilities and this was unanimously supported by the meeting.
"The board also reaffirmed its full support for the Scottish Rugby Executive management team."
Chairman Allan Munro added: "Scottish Rugby remains in excellent health and today's meeting simply demonstrates that the governance model of our game in Scotland is absolutely sound and is rightly held in high regard by other governing bodies.
"Further to unhelpful media speculation, the board also expressed confidence in the executive management team who have the full support of the board to drive forward the organisation.
"I am personally delighted with how our great sport is developing at all levels, and reiterate our thanks to all our staff, players and volunteers who work tirelessly to grow the game.
"I very much look forward with confidence to the Rugby World Cup later this year."
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