The greenback rose 0.24% versus a basket of its rivals to 97.47, its highest level since July 10.
"This takes the threat of yet another debt-ceiling drama off the table for two years, by which time many of us fervently hope that a set of rational politicians will have taken office and this whole pointless recurring drama will be done away with," said Marshall Gittler, chief strategist at ACLS Global.
The New Zealand dollar was the biggest loser after Bloomberg News reported that the country's central bank is refreshing its strategies for unconventional monetary policy.
The euro also struggled against the dollar but held firm at a two-year high against the low-yielding Swiss franc on rising concerns that the Swiss National Bank may intervene to weaken the currency.
While levels below 1.10 francs per euro is considered intervention territory, broadly unchanged sight deposits data from the SNB, the clearest indicator of the Swiss central bank purchasing francs, indicate authorities are not unduly worried about the Swiss currency's strength for now.
The dollar's gains were capped in a broadly rangebound currency market as investors waited for the outcome of policy meetings at the European Central Bank and the U.S. Federal Reserve in the coming days.
While the ECB is widely expected to signal a dovish policy stance at Thursday's meeting, the Fed is expected to cut interest rates by a quarter point next week.
The pound was the other notable loser in early London trading with the British currency sliding towards the mid $1.24 region ahead of the results of the Conservative Party leadership contest. Boris Johnson is widely expected to win and replace Prime Minister Theresa May.
Concerns that Britain will crash out of the European Union without a deal have grown after Johnson said he would pull Britain out of the European Union on Oct. 31 "do or die".
The pound traded at $1.2459, within striking distance of a 27-month low of $1.2382 reached last week.
"Johnson is expected to become the new prime minister, so there is a real chance of a hard Brexit," said Takuya Kanda, general manager of research at Gaitame.Com Research Institute in Tokyo.