The strike began earlier this week as management began laying off staff following an announcement that 35 out of 180 jobs would be cut at the national news provider, which supplies most of Switzerland's newspapers.
In an interview published in newspapers on Friday, Leuthard said the three-language agency was important for the diversity of the Swiss media.
As a consumer of its news, the government trusted the agency's high quality, she said.
Leuthard said the government had discussed the situation at SDA/ATS and supported funding the private agency to the tune of 2 million francs, however this would need to be approved by parliament.
The minister said newspaper publishers were facing huge challenges in the online market.
But she criticized them for launching free online products, saying journalistic output should not be free.
Instead print media should look for new business models and partners to cooperate with.
SDA/ATS workers have staged demonstrations against the cuts in Zurich, Bern and Lausanne.