All is quiet on the war -- and currency front. The Swiss franc and Japanese yen retreated from their recent peaks late Tuesday as investor's felt the odds of an all-out U.S. -Iran military showdown had waned.

The safe-haven yen dropped from a three-month high versus the dollar, though sentiment remains fragile due to ongoing jitters about a further deterioration in American-Irani relations.

The Swiss franc, another go-to currency, fell against the euro from four-month highs and declined against the dollar as a result of investor restlessness.

On Friday, a U.S. drone strike in Baghdad killed Iranian military leader Qassem Soleimani, widely regarded as the second most powerful man in Iran. Equity markets rebounded on Monday following news of the drone strike.

Since no more bad news from the Middle East followed since Friday, at least, the markets were somewhat calmed down and "panic movements like in the US dollar or the Japanese yen were reversed," analysts from Commerzbank said.

The US greenback was up 108.46 on the yen by 0.1 percent, leaving the Japanese currency somewhat out of its 107.77 high on Monday.

The Swiss franc fell by 0.4 percent to 0.9712 francs and by 0.2 percent to 1.0860 francs. The dollar rose, and dropped on Monday, with the euro dropping 0.2 percent to $1,1176.

The U.S. currency, the world's most liquid, is often bought in periods of market volatility, but its output has been inconsistent in recent sessions: Monday's marginally better than expected eurozone business survey data helped the euro.

The dollar index inched slightly to 96.712, against a host of other key currencies. The euro, on the other hand, was marginally swayed by data showing that inflation had risen in the European markets in December and retail sales were stronger than projected.

Recent survey results showed an increase in the eurozone's investor and business confidence. Also due later are U.S. trade balance results, manufacturing orders, and service sector numbers.

Other major currencies like the Sterling hovered around the $1.3160 mark ahead of the United Kingdom parliament buckling down to work again following the holiday break.

The onshore yuan has risen to a record of $6,9315 per USD for five months, an indication that traders are willing to put aside fears about a more serious clash between the US and Iran. The offshore yuan has gained 0.5 percent to 6,9293 per dollar; it's highest since Dec. 13.

The Australian dollar fell 0.9 percent to $0.6876, as investors were anxious about the economic impact of the country's deadly bushfires.

Meanwhile, It is reported that China and the US will sign a tentative agreement to de-escalate a protracted trade war on January 15.