NEW YORK (MarketWatch)—The U.S. dollar is on track for its strongest quarterly performance since 2008, gaining ground on the euro but losing some ground versus the Japanese yen.

The ICE U.S. dollar index DXY, +0.37%  , a measure of the U.S. unit against a basket of six major rivals, traded at 98.297 in recent action, up from 97.980 in North American trade late Monday. The index is on track for a quarterly gain of 8.9%, its strongest since a 9.6% rise in the third quarter of 2008, according to FactSet.

The dollar has risen in large part due to expectations for diverging monetary policy, with the U.S. Federal Reserve seen preparing to raise interest rates later this year as the European Central Bank, Bank of Japan and several other central banks continue to loosen policy.

Richmond Federal Reserve Bank President Jeffrey Lacker, a voting member this year of the rate-setting Federal Open Market Committee, on Tuesday said that unless incoming economic reports disappoint, “the case for raising rates will remain strong at the June meeting. Lacker has been one of the most hawkish members of the FOMC.

The dollar lost some ground versus the Japanese yen and has seen a muted performance versus the currency, which has been attributed in part to seasonal repatriation of profits by Japanese firms at the end of the country’s fiscal year.

The dollar USDJPY, -0.07%  traded at 119.85 yen, compared with ¥120.08 late Monday in New York. Earlier, the dollar had risen to a two-week high at ¥120.37. The dollar is up just 0.1% versus the Japanese currency over the course of the first quarter.

Market participants were expecting the greenback to have a downward bias against the yen as Japanese exporters and financial institutions made their final currency transactions on the day of book closing for the Japanese fiscal year.

“Investors don’t seem willing to make major moves, but they don’t want to sell the dollar much either,” says Marito Ueda, director at FX Prime byGMO. The fact the dollar hasn’t weakened against the yen may indicate the firmness of underlying demand, he added.

The ¥122-line has proved to be the recent sticking point for the USD/JPY, a mark the pair will need to cross first if it is to mount a challenge on ¥124.14, its high set on June 2007, Ueda said.

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“I don’t expect investors will push ahead with dollar selling in a positive manner over the mid-term” since the market has faith in the continued strength of the U.S. labor market, said Osao Iizuka, head of FX trading at Sumitomo Mitsui Trust Bank.

Economists surveyed by The Wall Street Journal expect 248,000 jobs were added in March. If the result matches those expectations it would be the 13th straight month of 200,000-plus job growth.

The market showed a muted reaction to comments by the Federal Reserve Vice Chairman Stanley Fischer. He said earlier Tuesday that Fed policy makers should start thinking further ahead. “We’ve got to start thinking about what interest rate determination will look like after we lift off” and begin raising rates, he said.

In other currency trade pairs, the euro EURUSD, -0.90%  was at $ 1.0774 from $ 1.0832, and has fallen nearly 11% versus the dollar over the course of the quarter. Against the yen, the shared currency EURJPY, -0.98%  traded at ¥129.09, down from ¥129.86.

The WSJ Dollar Index BUXX, +0.29% another measure of the dollar against a basket of major currencies, was up 0.3% at 87.83.