Oil prices fell in thin Asian trading, as traders looked ahead to talks in Geneva between the United States and Iran scheduled for later on Tuesday.

Brent crude fell towards $68 a barrel, after adding 1.3% on Monday, while West Texas Intermediate crude held above $63.

Iran's Revolutionary Guard forces are conducting naval exercises in the Strait of Hormuz, the vital waterway through which about one-fifth of the world's barrels of oil are transported, according to the country's semi-official Tasnim news agency.

Trading volumes are weak and negotiations are awaited.

Trading volumes were limited on Monday, with the number of Brent crude futures traded falling to its lowest level this year, as the US and Canada were closed for public holidays. Meanwhile, many Asian markets are celebrating the Lunar New Year this week.

Iranian Foreign Minister Abbas Araqchi held talks with the head of the UN nuclear watchdog and discussed proposals he will present in indirect talks with US Special Envoy Steve Wittkopf on Tuesday, according to Iranian state television.

US Secretary of State Marco Rubio said he was optimistic that Tehran and Washington could overcome years of confrontation and tension and eventually reach an agreement.

Geopolitical risks are putting pressure on the market.

Negotiations between Russia and Ukraine are also scheduled to take place in Geneva on Tuesday and Wednesday, but the prospects for a quick end to the nearly four-year-long conflict and the return of Russian barrel bombs appear slim.

ANZ Group Holdings analysts Brian Martin and Daniel Hynes wrote in a note: “The market remains volatile due to geopolitical uncertainty.” They added: “If tensions in the Middle East subside or significant progress is made in the Ukraine conflict, the risk premium currently priced into oil could quickly disappear.”

In the latest trading, Brent crude futures for April delivery fell 0.5% to $68.33 a barrel by 12:38 p.m. Singapore time. West Texas Intermediate crude futures for March delivery rose 1% from Friday's close to $63.50 a barrel. There was no settlement on Monday due to the Presidents' Day holiday.