The Dow Jones Industrial Average edged lower to 18,120, the broader S&P 500 index ended almost where it started at 2,139. The Nasdaq fell 0.2% to 5,235.
Traders are betting the US Federal Reserve will not raise rates after its meetings on Tuesday and Wednesday.
Traders are less certain about what action the Bank of Japan might take.
It also meets on Tuesday and Wednesday and some analysts think it may take further action to boost the economy.
"We're stuck in a trading range that we probably can't break out of until you get through the Fed meeting, and you get through probably the debate next Monday, and you get a lot closer to the next round of earnings releases," said Rick Meckler, president of LibertyView Capital Management.
"The market is resigned to the fact that the Fed won't move in September," said Matt Jones, head of US equity strategy at JP Morgan Private Bank in New York.
Oil prices made modest gains after Venezuela said both Opec and non-Opec oil producing countries were close to a deal to address the problem of too much oil on the market.
The price of Brent crude oil rose 0.3% to $44.91 a barrel, while US crude climbed 0.4% to $43.78.
Among individual shares, car giant General Motors rose 2.4% to $31.72, after Morgan Stanley raised its rating on the stock to "overweight".
(Close): There was an air of caution on Wall Street as traders awaited the outcomes of interest rate meetings in the US and Japan.