By Tommy Stubbington and James Ramage 

The dollar continued to surge Tuesday, buoyed by a slump in the euro as eurozone inflation sank to a five-year low.

The latest sign of sluggish price growth in the euro area is likely to crank up the pressure on the European Central Bank to further ease monetary policy, at a time when investors perceive that the U.S. Federal Reserve is edging toward raising interest rates.

Tuesday's gains were a continuation of the dollar's strength against the common currency, as a diverging outlook for the U.S. and Europe have supported the dollar while pushing the euro lower. The U.S. economy appears to be recovering, raising the possibility of higher interest rates and an end to dollar-crushing stimulus measures, while the eurozone struggles with sliding prices. The euro shed about 7.7% against the dollar in the third quarter, which ended Tuesday.

Early in the Americas session, the common currency pushed 0.9% lower against the buck to $1.2571, the lowest since September 2012. By the afternoon, the euro was down 0.4% at $1.2630.

Analysts said the decline in the euro triggered broader dollar strength, with the greenback rising 0.2% against the yen, to 109.66 yen, while the British pound slipped 0.2% versus the buck to $1.6213.

Consumer price inflation in the eurozone fell to 0.3% in September, data showed Tuesday. That marks the slowest rate since October 2009 and a fall even farther below the ECB's target rate of close to 2%.

"Given how important inflation readings are to the ECB's thinking, this figure will be a source of concern," said Phyllis Papadavid, a currency strategist at BNP Paribas. "We could see a more aggressive message at this week's meeting."

The central bank, which will make its October policy announcement on Thursday, has already stepped up efforts to head off the threat of deflation, with a surprise interest-rate cut in early September and plans to purchase bundles of private debt. But many analysts think the central bank will eventually have to opt for large-scale purchases of government bonds-known as quantitative easing-to pull the currency bloc out of its malaise. That prospect would further weaken the currency.

Meanwhile, the Fed will take its cues from a raft of indicators scheduled to arrive this week starting Wednesday. Specifically, the central bank will pore over numbers for wage growth and workforce participation within the Labor Department jobs report for September.

"We could see a pullback in the dollar, particularly if nonfarm payrolls come in below expectations on Friday," said Sireen Harajli, foreign-exchange strategist at Mizuho Bank. Soft employment numbers could persuade the Fed to delay raising interest rates as the U.S. economy recovers.

However, the dollar's fundamentals remain strong, so any decline would be temporary, Ms. Harajli said. "Right now there's every reason to buy the dollar and every reason to sell the euro."

For the third quarter, the dollar rose about 8.2% against the yen, while the British pound fell about 5.3% against the U.S. currency.

The Australian dollar, threatened by the possibility of higher interest rates in the U.S., fell about 7.2% against the greenback. The Aussie, as it is known, has benefited from U.S. interest rates near zero, which encouraged investors to borrow in U.S. dollars, sell those and then use the proceeds to buy assets denominated in the Australian currency.

--Write to Tommy Stubbington at tommy.stubbington@wsj.com and James Ramage at james.ramage@wsj.com