Brent crude rose 19 cents or 0.3pc to $70.30 a barrel by 0930 GMT, while US West Texas Intermediate (WTI) was up 50 cents or 0.9pc to $59.13 per barrel.
US crude futures were trading for first time since Friday due to a long holiday weekend.
Oil prices have been broadly supported by supply cuts by the Organization of the Petroleum Exporting Countries (OPEC) and its allies since the start of the year and helped by political tensions in the Middle East.
"Brent is likely to resume its upward trend in line with its fundamentals, which are tight," said Harry Tchilinguirian, global oil strategist at BNP Paribas in London.
"This tightness is reflected in the generic front-month Brent futures time-spread.
Backwardation is very steep at $1.33 a barrel - the last time we sustained such deep backwardation was in 2013, when spot Brent was trading above $100 a barrel."
Backwardation, a market structure where the spot price is higher than the price of crude in later months, tends to indicate tight supplies and a drawdown in inventories.
OPEC and some allies including Russia are due to meet on June 25 and 26 to discuss output policy.
Khaled al-Fadhel, oil minister of OPEC member Kuwait, said he expected the market to approach balance in 2019, as global inventories fall and demand remains strong.
"We still have some more work to do. I believe the market is expected to be balanced during the second half of 2019, more towards the end of the year", he told Reuters, adding the impact of US sanctions on Iran "has yet to be felt".
In physical oil markets, Middle East crude premiums hit their highest levels in years this month amid falling supply.
The United States has also imposed sanctions on Venezuela's oil exports.
But investors remained cautious because of the trade war between the United States and China, which could hit the global economy and dent fuel consumption.