Under the proposals each person would be given five self-test kits per months, as soon as reliable tests are available, the government said, while all tests at pharmacies and testing centres will be free of charge.
To ensure more testing is carried out, the government proposed to pay for the voluntary tests. It estimated the expanded testing scheme will cost more than 1 billion francs this year.
The dollar index was up 0.21% to 90.815 at mid-morning in New York, while the euro was off 0.36% to $1.209. Against the Swiss franc the dollar was up 0.45%.
The dollar may be more resilient in the near-term because "both growth and vaccination favour the U.S."
The Japanese yen weakened to a fresh 11-week low of 104.95 yen per dollar.
The Swiss franc broke lower from recent ranges to drop more than half a percent to its lowest against the buck since Dec. 2, at 0.8964 francs per dollar.
The yuan crept up after China's central bank lifted its official guidance level to the highest in 30 months , to as high as 6.5280 against the dollar in the onshore market, but was last unchanged at 6.5408.