Brent crude rose 63 cents to $64.34 a barrel by 1127 GMT. It is set for a monthly fall of more than 3%, however, due to lingering worries about oil demand.
US crude was up 46 cents at $57.33 a barrel, but also set for a monthly decrease of around 1.8%.
"Regarding the Fed, the market has priced in a 25 basis point cut for Wednesday," global oil strategist at BNP Paribas in London Harry Tchilinguirian told the Reuters Global Oil Forum.
"If the language we get from the Fed in post meeting comments is on the conservative, rather than accommodative side, the US dollar is likely to continue to remain strong and continue to present a headwind for an advance in oil."
While the Bank of Japan held off on expanding stimulus on Tuesday, it signalled its readiness to do so "without hesitation" if a global slowdown jeopardises the country's economic recovery.
US central bankers will begin their two-day meeting later on Tuesday and are expected to lower borrowing costs for the first time since the depths of the financial crisis more than a decade ago.
US President Donald Trump said a small rate cut "is not enough".
Economic growth in the United States slowed less than expected in the second quarter, strengthening the outlook for oil consumption but, elsewhere, disappointing economic data has increased concerns about slower growth.
US and Chinese negotiators also meet this week for their first in-person talks since agreeing to a truce to their trade dispute at a Group of 20 meeting last month.
However, expectations for progress during the two-day Shanghai meeting are low, so officials and businesses hope Washington and Beijing can at least detail commitments for "goodwill" gestures and clear the path for future negotiations.
Supply risks are still a concern as tensions remained high around the Strait of Hormuz, through which about a fifth of the world's oil passes.
BP has not taken any of its own oil tankers through the strait since a July 10 attempt by Iran to seize one of its vessels, the British company's Chief Financial Officer Brian Gilvary said on Tuesday.
Tensions spiked between Iran and the West after Iranian commandos seized a British-flagged oil tanker in the Gulf this month in apparent retaliation for the capture of an Iranian tanker by British forces near Gibraltar.