The dollar was not affected much after US President Donald Trump did not implement his threat to block an aid package for those affected by Covid-19 amid weak trading Monday due to holidays.
The pound sterling hovered below its highest level in two and a half years in Asian trading, after reaching last week a limited trade agreement for the post-Brexit era, which did not include the British financial sector.
The dollar index was little changed at 90.151, after falling for three days.
The pound rose 0.2% to $ 1.3565, heading back to the $ 1.3625 level it reached earlier this month for the first time since May 2018.
Trump signed pandemic aid and government spending totaling $ 2.3 trillion, to avoid a partial shutdown from Tuesday.
The euro settled at $ 1.2216, near its two-and-a-half-year high of $ 1.2273, which it touched this month.
The Australian dollar rose to 76.082 US cents, heading towards its highest level in two and a half years also at 76.390 cents, which it reached this month.
The yuan rose 0.1% in overseas transactions to 6.5200 per dollar, and it scored 6.5296 in the domestic market.
The dollar weakened slightly against the Japanese currency, recording 103.455 yen.