The national arts funding body acted after a number of companies were told their short-term fixed funding was to be axed and they would have to go through the project-based National Lottery.
Its move led to criticism from leading figures on the arts scene such as playwright David Greig and actor Alan Cumming.
Creative Scotland has also announced guaranteed funding worth £2.5 million for another six months.
In a letter to all the arts companies affected by the end of flexible funding (FXO), worth £7m a year in total, it pledged the money would be available until September next year.
It announced in May that companies, such as the CCA in Glasgow, would have their FXO status removed from next April and would instead have to apply for project-based Lottery funding. Those companies, which range from theatre to jazz and classical music to visual arts, sculpture and literature, will still have to apply for Lottery funding beyond September 2013, with deadlines in September and January this year.
Creative Scotland admitted its speed of change has been "over- ambitious" and its actions had "inadvertently caused anxiety".
However, the organisation is committed to its strategic direction and is unlikely to perform a complete U-turn on the removal of FXOs.
The letter from chief executive Andrew Dixon and chairman Sir Sandy Crombie states the continuation of funding until September 2013 will "provide time both to discuss organisations' strategic plans in the context of the art form reviews, where appropriate, and to confirm their future Lottery funding".
It adds: "This will ensure that organisations can plan with confidence and offer reassurance to their staff and boards."
"In practical terms this letter can be taken as a commitment to provide support up to six months at current FXO funding level from April 2013.
"However, in the event of an organisation making successful bids into the new Lottery funds we would reallocate this - grant back to our grant in aid budget.
"The concerns have substantially, though not entirely, been caused by the speed of change which has been over-ambitious, and we apologise that this has inadvertently caused anxiety amongst a number of arts organisations regarding their future."
The letter goes on to say that communication to artists and companies on future funding "has not been as clear as we would have liked", in particular, that organisations removed from FXO status will be able to bid for Lottery funding for up to two years, including their core running costs, which are a key concern of small to medium-scale arts organisations.
The body has also accepted that the way it has arranged for the funding changes to be run concurrently with reviews of the various arts sectors has been problematic.
It says: "We recognise that in our desire to see a longer period of research and consultation on the sector reviews, the review of the FXOs is now out of sync and that strategic commissioning and organisation plans would, in some cases, be better finalised once the outcomes of the relevant sector reviews are complete."
In his blog, Mr Dixon said the body, which funds the majority of arts activity in Scotland with £60m of funding a year, has revised its "core objectives to invest in artists and creative practitioners". He added: "This seeks to reinforce just how much we value their work and view them as central to a thriving arts and culture sector in Scotland."
At a board meeting last week Creative Scotland also approved a budget with increased resources for quality arts production, and national events including Homecoming and Glasgow 2014 and a four-year capital programme.