Downing Street has attacked meat retailers for keeping customers in the dark over the extent of the crisis.
A source at Number 10 questioned why most of the major supermarkets have failed to appear on TV and in the media generally to reassure shoppers.
Hundreds of Food Standards Agency test results are to be released shortly which could reveal the true extent of contamination in the UK.
In the meantime, Tesco has released the video on its website - but said it was recorded before Downing Street's comments.
CEO Philip Clarke promises a new approach in the video.
"I have asked my team to review our approach to the supply chain, to ensure we have visibility and transparency, and to come back with a plan to build a world class traceability and DNA testing system," he said.
"We are building a new website, which will enable our customers to see the progress we are making with our testing programme, and which products have been tested so you can be sure of where we are in the process.
"We pledge that over the weeks and months ahead, we will open up our supply chain, and give you more information than any retailer has before to enable you to make informed choices about the food you buy for your family."
Sky News has also approached several leading supermarkets to discuss their approach to the contaminated meat crisis.
Morrisons has been on the front foot with the media. Its statement said: "Morrisons has done numerous interviews on TV, radio and with newspapers, including on Sky News.
"We have done this because we want to keep our customers updated about how this scandal has affected Morrisons.
"So far we have had 68 test results in and no evidence of cross-contamination with horsemeat."
In response, Waitrose said: "We will not be giving any interviews today. We have been communicating with our customers - we have sent them letters. So far we have no positive results for horsemeat."
Asda's statement said: "We are waiting for the FSA announcements. We will provide a statement later possibly an interview. We have been continuously communicating with our customers."
The Co-operative Group said all tests on its products have come back negative for horse DNA.
"We are have commissioned stringent ongoing independent testing on our own-brand products containing minced beef, as agreed with the Food Standards Agency.
"Today's results have shown that, so far, no products in the current batch of those being tested have been found to contain horse DNA.
"Our tests are still ongoing and we continue to work with both the FSA and the British Retail Consortium, and expect to issue further updates in the next few days."
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