The dollar rose from a 15-year low against a basket of currencies on Wednesday as investors bet Federal Reserve's interest rate cut on Tuesday will help boost a slowing U.S. economy.

The Fed slashed the fed funds rate to 4.75 percent from 5.25 percent to help relieve strains in credit markets. While that has diminished the allure of dollar-denominated assets, initially sparking broad selling in the greenback, the move has improved the U.S. economy's near-term prospects.

A report showing the U.S. core consumer price index was in line with expectations in August had little impact, coming the day after Fed's decision. Similarly, a report showing U.S. home construction starts at their lowest in 12 years in August was largely ignored.

I think some people had lingering doubts with oil prices above $80 that prices could be a problem down the road, but these reports don't suggest that, said Michael Woolfolk, senior currency strategist at Bank of New York Mellon. They show the Fed has room to cut interest rates.

The euro fell 0.1 percent to trade at 1.3961 while the dollar slid 0.1 percent against the yen to change hands at 115.93.

The dollar index was up 0.2 percent at 79.33 after going as low as 79.091 earlier in the global session, according to Reuters data.

(Additional reporting by Steven C. Johnson)