WTI and Brent crude, the international benchmark, rose as protests stopped oil flows to Libya's eastern port and Saudi Arabia raised the official selling price for Arab Light grade crude to the U.S. and Northwest Europe. Brent was above $68 a barrel for the first time since December.
But price gains should be capped by any increase in output so oil prices may not go much higher for now. "Any increases in oil prices will bring more oil production, and it will dampen any price increases. Every time more production comes on, it is self-fulfilling. ... It will douse it and cool it off," said Gheit.
Read MoreOPEC likely to maintain policy in June: Delegates
Oil prices collapsed earlier this year after the Organization of the Petroleum Exporting Countries decided last November to let market forces determine the price of oil. Saudi Arabia made clear it would not cut its production while other higher cost producers, like the U.S. shale industry, continued to drill at full throttle.
Since then the Saudis have upped production to 10 million barrels or more a day, and U.S. oil production rose, then plateaued at around 9.3 million-9.4 million barrels a day. No change in OPEC policy is currently expected.
On Tuesday, Saudi Arabia oil minister Ali al-Naimi said he was not concerned by oil prices and that he was "not worried at all" about the prospect of Iranian crude coming back onto the market if sanctions on Iran are lifted as part of an international nuclear deal.
Read MoreOnly Allah knows about oil prices: Saudi oil chief
The U.S. industry, meanwhile, could be quick to gear up for a "fracking counterattack," said Andrew Lipow of Lipow Oil Associates. Lipow noted the forward futures show prices out in 2016 and 2017 to $65, $70 per barrel. "A lof of these frackers are thinking, 'Maybe I should hedge out in those years and start bringing rigs back on line at the end of 2015," he said. "I think anything over $60 is getting them interested in the Bakken and Eagle Ford."
The U.S. oil rig count fell to 679 as of last week, down from 1,527 at the same time last year. Besides shut-in wells, the industry could quickly get hundreds of of semicompleted wells up and running.
"This rally has been predicated in large part by the declining rig count impact on production. If we actually see production stabilize at around 9.4 million barrels a day, that's going to be bad news for the oil market because the producers were able to combat the decline in prices with better production efficiency and use of technology," Lipow said.
The fracking industry came under criticism from investor David Einhorn, chief of Greenlight Capital, on Monday at the Ira Sohn Conference. He described Pioneer Natural Resources as the 'mother fracker,' and "A business that burns cash and doesn't grow, (that) isn't worth anything."