Chances of a U.S.-Iran conflict escalating into something bigger are "very, very high" — though a full-blown war is unlikely, said a former energy advisor to the prime minister of Iran in the late 1970s.

Washington and Tehran nearly came to blows last week after Iran claimed it downed an American drone that entered its territory. The U.S. said its aircraft was operating in international airspace.

"We have to remember Iran is a regional superpower. U.S. says 'I'll put you in a box, please die.' They (Iran) are not going to stay in a box and just die," Fereidun Fesharaki, now chairman of oil and gas consultancy Facts Global Energy, told CNBC's "Squawk Box."

"They will strike back one way or the other; I think chances of tensions becoming bigger is very, very high in the near future," said Fesharaki.

In response to the downing of the U.S. drone, President Donald Trump ordered military strikes against Iranian targets on Thursday — but eventually halted those plans.

Escalating tensions between the two countries sent oil prices higher, with U.S. crude up more than 9% in the week, while the global benchmark Brent gained 5%. Investors fear an attack on Iran, a major oil producer and exporter, would disrupt energy flows from the Middle East — a region that provides more than a fifth of the world's oil output. Both oil indexes continued edging higher on Monday.

Chances of a conflict are at least 50% right now, said Fesharaki. It may not be a "full war," he pointed out, "but conflict which would disrupt (energy) supplies."

If Trump had carried out those military strikes as planned, the geopolitical risk premium on oil prices would have been $5 to $10 a barrel, said Fesharaki. Now, the geopolitical risk premium "is only one or two bucks at the moment, it's not really high enough," he added.