"No one with any credibility speaking for industry would be considering a delay," the minister for circular economy told MSPs on March 1.
Ms Slater, the Green co-leader, was responding to calls from within the SNP-Green coalition that the scheme should be delayed or stopped.
Fergus Ewing, the SNP's former economy minister, urged Ms Slater to call "a halt now" and "so save massive costs".
Mr Ewing, MSP for Inverness and Nairn, said: "This scheme may decimate small producers, hike beverage costs, damage the environment with millions of extra car miles, and a reduction in the amount of glass recycling for bottles, penalise local authorities, and cause massive job losses in small businesses whose life work will be ruined.
"Is the minister aware of the huge extra costs that will be incurred by businesses between now and mid-April: mid-April being when the new First Minister and cabinet could halt this scheme?
"Businesses have told me these extra costs will amount to, between now and April, £50 million for the convenience stores, between £10 million and £20 million for hospitality.
"A leading craft beer and wine online based retailer, based in Scotland, has stated that it will cost them comfortably six figures in the next six weeks. All wasted if this scheme is halted in April."
Among the three candidates seeking election as SNP leader and First Minister in April, Kate Forbes and Ash Regan have said they will pause the scheme, while Humza Yousaf will grant a one year grace period for small and medium-sized enterprises.
Earlier in her campaign, the current economy minister Kate Forbes had said: "The implementation of DRS needs to be paused and sense-checked, and that's what I'll do if I'm elected as leader." The SNP MSP for Skye, Lochaber and Badenoch added: "I believe in the principle, but the execution has to work too."
Ms Slater told Mr Ewing in the chamber: "The position of the Scottish Government is that this scheme will launch on August 16. (Mr Ewing) has outlined why this must be so, because businesses have invested over £300 million in Scotland towards its launch. They will get a return on that investment when those 20ps start flowing."
The Deposit Return Scheme (DRS) will require shoppers to pay an extra 20p when buying drinks in a single-use container made of PET plastic, steel and aluminium, or glass, between 50ml and three litres.
The fee will be refunded when they return the empty, intact containers for recycling at thousands of collection points, over the counter, via reverse vending machines, or an online retailer.
Producers had to register with the scheme's administrator Circularity Scotland Ltd (CSL) and its regulator SEPA, by a February 28 deadline, or they would not be able to trade.
The day after, Ms Slater informed the Scottish Parliament that an "overwhelming" 664 businesses had signed up, "representing over 90 per cent of the total volume of drinks containers sold in Scotland each year".
"There are still concerns among producers, and particularly the smallest companies affected by the scheme. I have consistently said that SEPA will take a flexible approach where possible. Producers can continue to register even now after yesterday's deadline."
She refused to answer how many producers had not registered, leaving opposition MSPs to make their own calculations.
The shadow minister for the economy, Tory MSP Maurice Golden, said: "The minister is deperately spinning the sign-up numbers, but the reality is it works out to barely 16 per cent of total number of producers. 664 out of 4,000 operating in Scotland.
"Small producers are appalled by the scheme roll-out and have not registered, which is why the Scottish Government has been forced to consider introducing a grace period."
A fellow Conservative MSP, Brian Whittle (South Scotland), quoted a letter from "a well known Scottish drinks producer" to Circularity Scotland, "which highlights their concerns around the continuing lack of clarity around advance payments, particularly given the comments from SNP leadership candidates, who all seem to take a different view from the minister on the scheme.
"The letter states: 'The methodology is not clear and has not been shared with us, so we do not know how our potential exposure can be calculated.'
"It goes onto make clear that they have only signed the producer agreement because they have been left with no alternative if they want to ensure they still have a Scottish business after August 16.
"Does the minister consider it acceptable that businesses are so frustrated with the lack of detail in this scheme that they're only prepared to sign up to it at economic gunpoint?"
Ms Slater replied: "Circularity Scotland exists to help Scottish businesses comply with the regulations passed by this parliament. I would encourage them to continue to work with Circularity Scotland."
A fellow Lothian MSP, Miles Briggs (Con), said: "These are small businesses. These are people who are having sleepless nights over this scheme, and these are people who believe this could drive their business to the wall. Can she apologise to these businesses?"
Ms Slater replied: "I hope businesses will be reassured by the announcement today, that the scheme has the confidence of their colleagues and of their competitors, and if they wish to continue to trade in Scotland, then they will engage with Circularity Scotland and SEPA. We will allow producers to continue to register with the scheme, and I encourage them to do so, so that they can continue to trade in Scotland."
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