The dollar retreated from a four-month high against the euro on Tuesday as risk appetite improved, following a weeklong rally as investors chased higher returns in the United States.

The S&P 500 and the Nasdaq opened at all-time highs on Tuesday after China's foremost medical adviser on the coronavirus outbreak said the epidemic may peak this month.

The death toll in mainland China from the outbreak climbed past 1,000 on Tuesday, but the number of new confirmed cases fell.

"There's been a bit of a disjoint with the way the equity market has been trading in the last couple of sessions and the way the FX markets have been moving, and I think to some degree we're seeing a bit of catchup on the FX side of things," said Bipan Rai, North American head of FX strategy at CIBC Capital Markets in Toronto.

Concerns about the economic impact of the coronavirus have added a safety bid for the greenback in recent sessions, while economic data has boosted the view that the US economic outlook is stronger than the euro zone's.

The dollar has also gained as low volatility across most of the foreign exchange market has encouraged investors to seek out carry trades, where they borrow in low-yielding currencies such as the euro and the franc and invest in dollars or other high-yielding currencies.

"One of the big prevailing narratives right now is for the carry trade," said Erik Nelson, a currency strategist at Wells Fargo in New York. "As volatility seems to be nonexistent in the FX market, a lot of people are piling into this short euro, long higher beta, higher interest rate currencies."

The euro fell as low as $1.0892 on Tuesday, the lowest since Oct. 1, before bouncing back to $1.0921.