West Texas Intermediate futures for October delivery rose 40 cents to settle at $68.99 a barrel on the New York Mercantile Exchange.
Also weighing on oil prices, US drillers added two oil rigs in the week to December 1, bringing the total count up to 749, the highest since September, General Electric Co's Baker Hughes energy services firm said on Friday.
Official U.S. government data is due to be released on Wednesday. Barkindo said a "permanent" framework of cooperation between the 14 OPEC members and 11 non-OPEC oil states, including the world´s top producer Russian Federation, was expected in December.
Asked whether a deal between OPEC and other producers, a group known as OPEC+, could discuss increasing output from levels agreed in June, Novak said: "I think we have the possibility to discuss any possible scenarios".
For example, prices could weaken if China retaliates by cutting off the USA supply chain for raw materials and small components for US made technological devices. On Tuesday, the global oil benchmark rose 1.3 percent on a media report that Saudi Arabia, the world's largest oil exporter, was comfortable with prices above $80, indicating the producer would not try to increase output to drive prices lower.
Bloomberg reported on Tuesday, citing unnamed Saudi sources, that the kingdom was now comfortable with prices above $80 per barrel, at least for the short term.
The news agency reported while Saudi Arabia had no desire to push prices higher than $80/Bbl, it may no longer be possible to avoid it. US sanctions affecting Iran's petroleum sector are due to come into force from November 4.
Oil futures also drew support from geopolitical risk on Tuesday.
USA crude inventories rose by 1.2 million barrels to 397.1 million in the week to Sept 14, according to data released on Tuesday by the American Petroleum Institute (API).
U.S. President Donald Trump on Monday said he would impose 10 percent tariffs on about $200 billion worth of Chinese imports.
The tariffs are likely to limit economic activity in both China and the U.S. and that should lower oil demand growth as less fuel is consumed to move goods for trade.
Oil prices slipped on Tuesday morning in Asia as the USA vowed to impose 10% tariffs on a further $200 billion worth of Chinese goods on Monday, which rattled the markets.