The upward momentum in the global benchmarks gathered pace in afternoon trading. International Brent crude oil futures were up $1.31 at $61.24 a barrel by 1438 GMT and on track for its biggest monthly rise since April 2016.
US West Texas Intermediate (WTI) crude futures were up $1.32 at $53.31.
Venezuela has the world's biggest proven oil reserves, but its potential has not been realised fully because of a lack of investment. The country is also a member of the Organization of the Petroleum Exporting Countries, which is implementing a supply cut deal to shore up prices.
"The Latin American country is predominantly the producer of heavier crude, exactly what (US Gulf) refiners are thirsty for," PVM said in a note.
"They will now have to turn elsewhere (possibly to Mexico, Saudi Arabia and Iraq) to satisfy their needs for this type of crude, which would inevitably lead to a price spike."
Venezuela's exports fell to little more than 1 million barrels per day (bpd) in 2018 from 1.6 million bpd in 2017, according to Refinitiv ship-tracking data and trade sources.
The United States has been the biggest buyer of Venezuelan oil despite their political differences, taking about half of the country's export volumes, followed by India and China.
Petromatrix estimated that Venezuelan exports will drop by about 500,000 barrels per day under current conditions.
Meanwhile, Libya's biggest oilfield, El Sharara, will remain shut until departure of an armed group occupying the site, the head of National Oil Corp said.
However, global oil supply remains high, largely because of a more than 2 million bpd increase in US crude oil production <C-OUT-T-EIA> last year to a record 11.9 million bpd.
"(The) focus will be intensifying on the US inventory data tomorrow, with expectations of a further build in stocks," Cantor Fitzgerald Europe said in a note.
There are also concerns in the oil industry that crude demand could stutter.
Activity in China's vast manufacturing sector is expected to shrink for the second straight month in January, a Reuters poll showed.
Warnings from Caterpillar and Nvidia on Monday about weakening demand from China have also concerned investors.