The U.S. dollar declined against its major counterparts in early European deals on Tuesday, as treasury yields fell in the wake of mounting geopolitical tensions over North Korea and Middle East.

North Korea warned of 'catastrophic consequences' to the U.S. government's 'outrageous actions' to deploy Navy strike group to the Korean Peninsula.

The deployment showed Washington's "reckless moves for invading had reached a serious phase," the foreign ministry said, adding that North Korea is ready to defend with any mode of war.

Separately, U.S. President Donald Trump and British Prime Minister Theresa May have agreed there is a "window of opportunity" to persuade Russia to break ties with Syrian President Bashar Al-Assad.

Trump is open to authorizing additional strikes on Syria if the regime uses chemical weapons again or deploys barrel bombs in the country, the White House had said on Monday.

The benchmark yield on 10-year note fell 2.35 percent, while that of 2-year equivalent was down by 1.25 percent. Yields move inversely to bond prices.

Speech at the University of Michigan on Monday, the Fed Chair Janet Yellen hinted at raising rates at a gradual pace as the central bank is targeting full employment and near 2 percent inflation without letting the economy overheat.

With the day's economic calendar being light, investors focus on producer prices and University of Michigan's consumer sentiment index on Thursday and consumer prices and retail sales on Friday for more clues about the health of the U.S. economy.

The greenback held steady against its major rivals in the Asian session, with the exception of the yen.

Reversing from an early high of 1.0094 against the franc, the greenback slipped to a 4-day low of 1.0066. If the greenback extends slide, 0.98 is possibly seen as its next support level.

The greenback fell to 1.0605 against the euro, from an early high of 1.0579. The greenback is poised to challenge support around the 1.07 mark.

The greenback declined to a 4-day low of 1.2444 against the pound, compared to 1.2416 hit late New York Monday. On the downside, 1.255 is likely seen as the next support level for the greenback.

Data from the British Retail Consortium showed that U.K. like-for-like retail sales slid 1.0 percent on year in March.

That missed forecasts for a decline of 0.3 percent following the 0.4 percent decline in February.

The greenback that closed yesterday's trading at 110.91 against the yen slipped to a 4-day low of 110.46. The greenback is seen challenging support around the 106.00 area.

The greenback retreated to 0.7513 against the aussie, from an early high of 0.7494. The currency is thus heading to pierce its early 4-day low of 0.7513. Continuation of the greenback's downtrend may see it challenging support around the 0.78 region.

The greenback hovered at an Asian session's 8-day low of 1.3314 against the loonie, compared to Monday's closing value of 1.3325. The next possible support for the greenback-loonie pair is seen around the 1.30 level.

In the New York session, U.S. NFIB small business index for March is slated for release.

At 1:45 pm ET, Federal Reserve Bank of Minneapolis President Neel Kashkari is expected to speak at the Minnesota Business Partnership, in Minneapolis.

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