The Japanese yen and Swiss franc eased off earlier highs as fears about the economic fallout from the coronavirus outbreak in China waned, though the dollar index held near two-month highs.

Global markets had stabilized somewhat after a risk sell-off which ran from Monday through Tuesday morning. The Japanese yen

was last 0.22% weaker at 109.13 per dollar, having hit a 2-1/2-week high on Monday. The Swiss franc was 0.36% weaker against the dollar, last at 0.973.

Earlier Tuesday the Swissie had strengthened to 1.067 francs per euro, its highest since April 2017.

"If there's anything driving things, it seems just to be the fading of concerns around the coronavirus. This is based on more reports that the Chinese are clamping down," said Thierry Wizman, global interest rates and currencies strategist at Macquarie Group.

President Xi Jinping said on Tuesday that China was sure of defeating the "devil" coronavirus, which has killed 106 people. Yet despite his confidence, international alarm has risen: From France to Japan governments organized evacuations, while Hong Kong planned to suspend rail and ferry links with the mainland.

Global stock markets and oil prices have tumbled in recent days on fears the virus could further damage China's already weakened economy. That also briefly inverted the three-month, 10-year US Treasury yield curve, considered a fairly reliable recession predictor.

By Tuesday afternoon, however, US stocks and Treasuries yields had turned around and the offshore yuan saw some relief. The Chinese currency firmed 0.24% versus the dollar, rising off three-week lows.

The dollar index, another safe-haven asset, was slightly off the two-month high hit earlier in the day, but remained in demand on Tuesday afternoon. It was last trading up 0.4% on the day at 97.995.

"With much of Asia closed, I think maybe foreigners are feeling like the only way they can get exposure to global stock markets in view of the better news on the virus is simply to buy the US market because China is closed, Hong Kong is closed. Maybe that's why the dollar is stronger. If that's the case, then that would reverse at the time that the other markets open up again for trading," said Wizman.

The Federal Reserve began a two-day policy meeting on Tuesday, at which it is largely expected to reiterate that interest rates will remain on hold this year.