The greenback took another hit on Tuesday after the Republican health-care bill aimed at replacing Obamacare failed to get enough backing to proceed to a debate.

The dollar index, which measures the greenback against a basket of currencies, extended its recent tumble, falling as low as 94.818 in Asia trade on Tuesday, from a high as 95.191 prior to the news the current version of the bill was dead on arrival — or at least in for major surgery.

That was the index’s weakest since September of last year, prior to the U.S. presidential election, and the levels compared with the dollar index trading as high as 95.348 on Monday, and 95.834 on Friday.

Two more Republican senators said on Monday they will oppose the current Republican health-care bill, bringing the total to at least four. The GOP holds 52 seats in the Senate, and the defections meant there weren’t enough votes for a motion to proceed — a procedure that would start debate on the bill.

Republicans were tackling the health-care overhaul before tax reform, another key campaign plank, as many of the cuts in health-care spending were earmarked to finance the proposed tax alterations.

Analysts have viewed every setback to the health-care bill as delaying the party’s broader agenda.

Among other currencies, the yen climbed against the dollar, with the greenback fetching as little as 112.14 yen in Asia trade on Tuesday, down from as high as 112.70 yen earlier, compared with levels well over 113 yen last week.

The euro climbed as high as $1.1531 in Asia trade on Tuesday, up from $1.1470 earlier in the session, touching its highest levels since May 2016.

The Australian dollar surged to its highest since mid-2015, trading as high as $0.7873 in Asia trade on Tuesday, up from $0.7783 earlier in the session.

—CNBC’s Jacob Pramuk contributed to this article.