The dollar index, which measures the greenback against six major peers, rose 0.06 percent at 104.2663 in late trading.
The White House and House Republicans inked a deal on federal government debt ceiling on the weekend, lending support to the U.S. dollar in contrast with euro.
The narrowing of U.S. credit default swaps (CDS) over the short term indicates reduced concerns about a U.S. debt default, which could strengthen the U.S. dollar and exert downward pressure on the exchange rate of euro against the U.S. dollar, said James Hyerczyk, senior market analyst with market information supplier FX Empire.
Still, the U.S. dollar weakened against most of other major currencies as risk appetite improved.
The thin trading during U.S. Memorial Day holiday led to narrow fluctuation of major pairs of foreign exchange rate on Monday.
In late New York trading, the euro was down to 1.0709 dollars from 1.0730 dollars in the previous session, and the British pound increased to 1.2357 dollars from 1.2350 U.S. dollars in the previous session.
The U.S. dollar bought 140.3940 Japanese yen, lower than 140.6220 Japanese yen of the previous session. The U.S. dollar fell to 0.9041 Swiss francs from 0.9047 Swiss francs, and it fell to 1.3593 Canadian dollars from 1.3615 Canadian dollars. The U.S. dollar rose to 10.8185 Swedish Krona from 10.8130 Swedish Krona.
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