The Fed is expected to keep borrowing costs on hold but its economic commentary will be closely scrutinised for hints about future moves.
In Japan, the benchmark Nikkei 225 index closed down 0.8% at 16,974.45.
Shares of Japanese consumer electronics firm Sharp slumped nearly 12% on reports a takeover deal may be delayed.
According to Reuters, Taiwan's Foxconn - also known as Hon Hai Precision - may postpone its $6bn (Â£4.2bn) purchase of Sharp after receiving "new material information" and is requesting more guidance on its latest quarterly performance.
In China, the Shanghai Composite index rose 0.2% to 2,870.43 while Hong Kong's Hang Seng index dropped 0.15% to 20,257.70.
In Australia, the S&P/ASX 200 index ended 0.15% higher at 5,119.03 even though falling iron ore prices dragged on mining shares.
South Korea's Kospi closed up 0.3% at 1,974.90, despite data showing the unemployment rate hit a five-year high.
The rate rose to 4.1% from 3.5% in February, which was higher than economist expectations, due to a contraction in the manufacturing and construction sectors.
However, analysts say most global investors are focusing on the outcome of the Fed's meeting.
"Another hike is sharply at odds with Fed concerns about increased uncertainty around global/China outlook and market turbulence tightening credit conditions," said Vishnu Varathan from Mizuho Bank.
He added that attention was focused on any hints the bank might make about the frequency of interest rate rises this year.
Asia markets were mixed on Wednesday as investors waited for the outcome of the latest Federal Reserve meeting.