The US Federal Reserve is not expected to raise rates on Wednesday, but all eyes will be on whether it gives any clues as to the timing of rate rise.
The Bank of Japan meets on Friday and there has been speculation it might expand its stimulus programme.
Japan's benchmark Nikkei 225 closed down 0.9% at 18,777.04.
In Australia, the benchmark S&P/ASX 200 finished the day barely changed, down just 0.03% at 5,346.20.
Shares in one of the country's biggest lenders, National Australia Bank (NAB), were halted from trade on Tuesday.
The announcement on the Australian Securities Exchange was made pending news of a "material transaction". The bank had been discussing a possible life insurance deal with Nippon Life Insurance.
NAB is due to release its full year results on Wednesday when it is also expected to update the market regarding its plans to exit its operations in the UK.
In South Korea, the benchmark Kospi index closed down 0.17% at 2,044.65.
In China, shares traded mixed with the Shanghai Composite closing up 0.1% at 3,434.34, while Hong Kong's Hang Seng index ended down 0.1% at 23,142.73.
Shares in Asia fell, with investors remaining cautious ahead of meetings of the US and Japanese central banks later in the week.