The West Texas Intermediate (WTI) for February delivery dropped 0.96 dollar to settle at 58.08 USA dollars a barrel on the New York Mercantile Exchange.
Brent crude was up 1 cents at $64.99 per barrel at 0737 GMT, while West Texas Intermediate (WTI) crude was up 5 cents at $59.09 a barrel from the previous session.
Oil prices edged down on Monday as fears of conflict between the United States and Iran eased, although the decline was checked by the planned signing of an initial US-China trade deal this week, which could boost demand.
Mnuchin described the agreement as "very, very extensive", although the deal will not completely resolve the trade dispute between the USA and China. China has pledged to buy more than $50 billion in energy supplies from the United States over the next two years, according to a source briefed on the trade deal.
Still, with traders already pricing in the signing of the deal, there is more downside risk to prices, said Michael McCarthy, chief market strategist at CMC Markets.
This means that is highly likely that crude oil prices may remain stable at least until Nov 2020, when the US Presidential elections are due.
"It's hard for crude oil to go higher if refiners continue to lose money or at best break even on gasoline", said Tom Kloza, global head of Energy Analysis at Oil Price Information Service (OPIS).
USA crude inventories were expected to have fallen last week, while gasoline stocks were set to gain for the tenth straight week, a preliminary Reuters poll showed Monday.
Elsewhere, Saudi Arabia's energy minister Prince Abdulaziz bin Salman said his country will work for oil market stability at a time of heightened U.S.
Oil prices surged to their highest in nearly four months after a USA drone strike killed an Iranian commander on January 3 and Iran retaliated with missiles launched against US bases in Iraq. The threat of an outright war has receded since Tehran fired missiles at US-Iraqi bases last week in retaliation for Washington's assassination of its top general.