Brent crude oil futures were up 19 cents, or 0.3%, at $69.65 a barrel by 0517 GMT, while West Texas Intermediate (WTI) was up 18 cents, or 0.3%, at $66.45 a barrel.
Both contracts rose more than 1% on Monday.
U.S. President Joe Biden will send at least 20 million more COVID-19 vaccine doses abroad by the end of June, marking the first time the United States is sharing vaccines authorized for domestic use.
The British economy reopened on Monday, giving 65 million people a measure of freedom after a four-month COVID-19 lockdown. And with accelerating vaccination rates, France and Spain have relaxed restrictions, and Portugal and the Netherlands have opened up travel.
In the United States, New York state will no longer require masks in most public spaces for people fully vaccinated against COVID-19 as of Wednesday, and other regions are opening up their economies as well.
In Asia in contrast, Singapore reported the highest number of local infections in months and Taiwan saw a spike in cases, and both countries have reinstituted lockdown measures.
In India, the second-hardest hit by the pandemic, domestic sales of gasoline and diesel by state refiners plunged by a fifth in the first half of May from a month earlier as pandemic lockdowns hit industrial activities and consumption, preliminary data showed on Monday.
With regard to the Iran-U.S. talks, as the United States tries to reinstate the 2015 Iran nuclear deal, it is tiptoeing through a minefield of sanctions put down by former U.S. President Donald Trump after he abandoned the deal three years ago.