In a Saturday letter to the bill's other two co-authors, Sens. John Kerry, D-Mass., and Joseph Lieberman, the Connecticut independent, Graham said he would stop participating in negotiations on the climate bill, The New York Times reported.
Graham complained debate on immigration reform would shift the focus away from national energy and global warming.
His withdrawal from negotiations came after months of work on the bill with Kerry and Lieberman, and the three had been scheduled to announce it Monday morning in Washington. The announcement has been postponed indefinitely.
Graham, who has worked with Democrats on immigration and was expected to offer GOP support on the issue, wrote Democrats appeared to be rushing immigration legislation in response to anti-immigrant sentiment, including the strict new Arizona law on illegal immigrants.
"Moving forward on immigration -- in this hurried, panicked manner -- is nothing more than a cynical political ploy," Graham wrote. "I know from my own personal experience the tremendous amounts of time, energy and effort that must be devoted to this issue to make even limited progress."
Kerry said in a statement he would be ready to resume work on the climate bill when Graham got back into the discussion but didn't predict when that would be.
"We will continue to work, and we will do everything necessary to be ready when the moment presents itself," Kerry said.