Speaking at High Barlay near Gatehouse of Fleet, Richard Lochhead said the Scottish Government would give more support to farmers once the scale of the losses to farmers was known but stopped short of outlining what sort of support it would be or how much.
"We are working with the industry to measure the damage caused by the weather to agriculture in south-west Scotland.
"We want to make sure businesses can remain viable and help farms recover. We will make more support available once we understand the scale of the damage.
"It's clear there has been significant economic losses."
He urged banks and landowners to "lend a sympathetic ear", adding it had been a disaster for farmers.
The Scottish Government has already provided £500,000 to help farmers pay for collection of dead animals lost in the snow.
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High pressure brings a mainly dry spell. Winds become lighter. Feeling warmer in any sunshine during Wednesday
The second of our special reports looks at the history of the Borders Railway - starting with the closure of the Waverley Line in 1969.
Predominantly dry over the coming few days with variable cloud & some sunshine. Cool nights but daytime temperatures recovering a little