The draft strategy, issued in July, suggested there were plans to cut maintenance to all but 28 large "focal" parks, with the remaining green spaces to feature meadows and a "rethinking" of sport and play facilities. Council bosses moved to clarify the report after a public outcry.
Among the proposed changes, 28 parks within the borough were to become 'main' sites, meaning they would be within a one mile walk of all local urban communities. They would become the focal point of the green space "offering" in each area and would have the same or better facilities as they currently have.
But the remaining open spaces in each area would see changes in management and maintenance. This could include "the introduction of long grass and meadow areas, the redesign of other horticultural and park features, and rethinking sport and play facilities".
At the time, Cllr Ian Moncur said the strategy was "definitely not" about "ripping out children's play areas" but about "how we better manage our parks and greenspaces in [the] face of further cuts".
He said the report had been taken out of context which had caused "distress" to residents.
Cllr Moncur has now asked for a revised report to be written before any consultation starts.
Moncur, who is cabinet member for health and wellbeing, said: "We are extremely lucky in Sefton to have so many parks and open spaces, many of which are recognised through the Green Flag award scheme.
"In the last five years alone since the parks have been in my portfolio, we have witnessed a significant amount of investment and development in them.
"This includes more than £1.5m of new capital investment and £500k has been invested in providing parts and maintenance to our sites. In real terms we now have 16per cent more equipment in our parks than we did 5 years ago.
"Despite public parks having seen a reduction in budget, we have maintained a strong commitment to providing good opportunities for play.
"Obviously our parks and greenspaces mean so much to so many people in Sefton and beyond, and I want to make sure any consultation on the future of them is carried out as widespread as possible.
"We are not looking to close any parks in Sefton - far from it, this is about moving forward in the way we run them in the face of severe Government cuts.
"No decisions have yet been made and when we get to the point of consulting on this important topic, I sincerely hope local communities, partners and volunteering groups use the opportunity to propose ways in which they can help maintain their local parks and assets for the future.
"We have listened and want to get this right as we look to develop our many great parks and greenspaces for the future."
Sefton Council is having to find a further £64m worth of savings between 2017/2020 and is looking at how it provides numerous services across the borough.