President Obama said that the rule could constitute a regulatory burden for the still-struggling economy, especially since the EPA was already scheduled to review the standard in 2013.
The EPA is expected to issue a new proposal later this year.
The gas and oil industry is worried that it will hurt businesses and could send the country back into recession without increasing public health.
"These could be the costliest EPA regulations ever," Howard Feldman, the American Petroleum Institute's director of regulatory and scientific affairs, told reporters on Thursday.
Current ozone standards allow for 75 parts-per-billion, but 46 areas across the country have not yet met that limit.
"We think those areas should be working on achieving the 2008 standard before we change the standard now — before we even consider changing it now," Feldman said.
When the White House pulled the plug on the EPA's proposal in 2011, the agency was seeking a standard of 70 parts-per-billion.
If the standard is reduced to 60 parts-per-billion, as some of the EPA's advisory committees have proposed, even "pristine locations" like Yellowstone National Park might not meet it, Feldman warned.
Health groups including the American Lung Association and the American Medical Association have disagreed, and in 2010 said that the 60 parts-per-billion level "will provide the strongest protection for public health."
Last year, a study partly funded by the EPA found that the lowest standard could prevent up to nearly 8,000 premature deaths each year.
-- This story was updated with additional information at 1:20 p.m.