US West Texas Intermediate crude for June delivery was up 24 cents, or 0.4 per cent, at $ 68.81 a barrel by 0402 GMT, after settling up 47 cents on Monday.
London Brent crude for new July delivery was up 21 cents at $ 74.90. The June contract expired on Monday, settling up 53 cents at $ 75.17.
Trade was quiet in Asia as many markets including China, India and Singapore were closed for public holidays.
Oil prices jumped on Monday after Netanyahu stepped up pressure on the United States to pull out of the 2015 nuclear deal with Iran, presenting what he called evidence of a secret Iranian nuclear weapons programme. Tehran has denied ever seeking nuclear weapons.
Trump has given Britain, France and Germany a May 12 deadline to fix what he views as the deal’s flaws or he will reimpose sanctions.
“(Global oil markets are) roughly in balance now, but if the deal were not renewed, Iranian oil exports could plunge, which would lead to a complete supply shortage,” said Tomomichi Akuta, senior economist at Mitsubishi UFJ Research and Consulting in Tokyo.
“If that happened, Brent prices could jump to near $ 90 (a barrel).”
Oil prices stood within $ 1 of a more than three-year high hit in late April amid concern over the potential disruptions to Iranian crude flows. Analysts said the market is extremely sensitive to any developments on the nuclear deal and sanctions.