Graham is one of three senators co-sponsoring a comprehensive energy and climate bill scheduled to be unveiled on Monday. But in a letter Saturday to Senate leaders, Graham said he will withdraw his support for the climate measure if Reid moves forward on immigration first.
"Unless their plan substantially changes this weekend, I will be unable to move forward on energy independence legislation at this time," Graham said in a written statement. "I will not allow our hard work to be rolled out in a manner that has no chance of success."
Reid has said he wants to pursue legislation offering legal status for many unlawful immigrants before tackling climate change.
"Immigration and energy reform are equally vital to our economy and national security and have been ignored for far too long," Reid said Saturday in response to Graham's criticism.
"I appreciate the work of Sen. Graham on both of these issues and understand the tremendous pressure he is under from members of his own party not to work with us on either measure," he said. "But I will not allow him to play one issue off of another, and neither will the American people. They expect us to do both, and they will not act accept the notion that trying to act on one is an excuse for not acting on the other."
Graham called Reid's apparent shift toward immigration "a cynical political ploy" that could derail months of effort on climate change.
"Let's be clear, a phony, political effort on immigration today accomplishes nothing but making it exponentially more difficult to address in a serious, comprehensive manner in the future," he said.
The Associated Press contributed to this report.