Markets in Tokyo and Sydney opened sharply higher early Wednesday, rebounding from Tuesday’s continued losses and building on the momentum of the U.S. stock market rally.

Japan’s blue-chip Nikkei 225 average opened up 1.9 percent, putting it well above the 9,000 it left during Tuesday’s heavy selling. Australia’s Standard & Poor’s /ASX 200 index was up almost 1 percent on the opening bell, putting it on track to recover from Monday’s close of 3,986.10, the lowest in more than two years.

Asian markets ended Tuesday down sharply lower, with several markets, including Hong Kong, South Korea and Singapore, losing more than 3 percent on fears of the continuing fallout from the European debt crisis and the global economic slowdown. If they continue to recover, that could fuel more confidence in U.S. markets when trading resumes Wednesday.