Brent crude futures edged up 6 cents, or 0.07%, to $90.44 per barrel by 1156 GMT. U.S. West Texas Intermediate (WTI) crude futures were down 2 cents or 0.02% at $86.41, Reuters reported.

On Monday, Brent posted its first decline in five sessions and WTI its first in seven as a fresh round of Israel-Hamas ceasefire discussions in Cairo spurred prospects of a breakthrough.

Those hopes faded after Israeli Prime Minister Benjamin Netanyahu said a date had been set for Israel's invasion of the Rafah enclave in Gaza, IG analyst Tony Sycamore wrote in a note.

The continuation of the conflict keeps alive the risk that other countries could be drawn in.

Mexico's state oil company Pemex said it would reduce crude exports by 330,000 barrels per day so it can supply more to domestic refineries, cutting the supply available to the company's U.S., European and Asian buyers by one-third.

Pemex had already cut its April exports by 436,000 bpd.

Investors are also awaiting inflation data due from the U.S. and China for further signals on the economic direction of the world's top two oil consumers, as well as an interest rate decision from the European Central Bank on Thursday.

"The fate of interest rates and if there can be a reduction in 2024 is at stake and the rally in oil is making it harder for anyone believing that inflation is under control," said PVM analyst John Evans.

Vitol CEO Russell Hardy at a conference in Switzerland said he expected oil prices to trade in a range on $80-100 a barrel and oil demand growth of 1.9 million bpd in 2024.