Retailers have confirmed to Environment Secretary Owen Paterson that they expect the majority of their tests on processed beef products to be completed by Friday.
Retailers and the British Retail Consortium (BRC) met Paterson for the first time since test results covering 65% of the targeted products were published Friday.
Speaking after the meeting, the BRC also said that retailers are doing all they can to engage with consumers on the issue and establish the extent and causes of failures in the supply chain.
The last report said five brands tested positive for horse meat against the Food Standards Agency's threshold. These are the five own brand products that have already been notified to the FSA and withdrawn from sale over the same period.
Failures in the supply chains of supermarkets were highlighted by farming groups like the National Beef Association.
"The squeezing of their suppliers margins and the relentless search for profit through buying cheaper product is the reason horsemeat is in their products" the association said.
"The supermarkets spend millions on creating and protecting their brand but what is behind that brand is reflected in their own brand economy burgers. They are brands are funded by the exploitation of the consumer and the supplier.
"Supermarket own brands contained horsemeat and as such it is their name on the packet and their responsibility to be sure what is in the product. They cannot blame anyone other than their own buying policies for their failure to supply their consumers with what it says on the label."
British Retail Consortium Director General Helen Dickinson said: "Test results have continued to come in over the weekend. The labs are working flat out and our members are confident that the vast majority of testing will be completed by Friday.
"We were very pleased that the Secretary of State recognised the hard work of retailers in progressing their testing programmes so quickly.
"Retailers take their responsibilities very seriously and are doing everything they can to maintain consumer confidence and increase surveillance.
Farming groups have blamed retailers who 'habitually drive down meat prices' below the cost of production causing a lapse in quality or an adulterated content of the product.
"Where on earth do they think this cheap euromeat is coming from?" demanded Richard Longthorp, chairman of the NPA.
"If you consistently buy something below the price at which it can be produced, you must know that corners have been cut in quality, or safety, or legality, or all three."
NPA general manager Dr Zoe Davies said: "even though cheap imported europork hasn't been implicated in the Horsegate scandal, the price that British pig farmers get for their safe, high-quality product plummeted by an unprecedented 3p a kilo on Friday."
"Our pig farmers are already making a loss as supermarkets import increasing quantities of cheap pork from the continent and for some this latest blow may well be the straw that breaks the camel’s back."
"But that’s not good enough for some of our largest retailers. They have to buy cheap-cheap-cheap, and that is what has landed the High Street in its current fear and confusion."
Over 90 percent of British pork is independently audited through the Red Tractor assurance scheme along its entire production process, from the feed that the pigs eat, to the way they are housed and cared for, to the way they are electronically-tracked to meat plants, and to the way the meat is processed, packed and labeled.
"Shoppers can no longer trust many supermarkets but they can trust British meat."
But Dickinson said: "Members are meeting every day with the Food Standards Agency and working around the clock to understand what has happened and act on lessons learned.
"Our top priority is to continue to engage with our customers and reassure them that we have effective solutions to the issues that have come to light. Retailers are using every available channel for direct dialogue with their customers, from social and traditional media to answering questions in-store.
"It's clear that there will be things that need to change for the future as a result of these incidents. Retailers are scrutinising their systems and processes, alongside intelligence gathering and sharing to identify practical improvements that will turn the lessons learned into action."