Investors are also gearing up for next week's high-stakes G20 summit, where US President Donald Trump is set to meet Chinese counterpart Xi Jinping on the sidelines to discuss their trade war.
In initial deals, London's benchmark FTSE 100 index rose 0.2 percent to 7,369.50 points, compared with the closing level on Monday.
On the downside, in the eurozone, Frankfurt's DAX 30 shed 0.1 percent to 12,069.37 points and the Paris CAC 40 nudged 0.1 percent lower to stand at 5,386.38.
"European markets are treading water at the open, a further sign of nerves from investors as we near the Fed policy meeting on Wednesday," Oanda analyst Craig Erlam told AFP.
The Federal Reserve is expected to give further hints about what would be the central bank's first rate cut in more than a decade.
The Fed has raised rates nine times over the last three and a half years as the economy recovered and put millions of Americans back to work.
"So much has been priced in at this stage that it's going to be tough for the central bank to live up to market expectations," added Erlam.
"Ultimately, how they see the year out will likely largely depend on trade talks between the US and China, with the next opportunity to overcome the impasse being the G20 next week."