Kerry said after more than six months of meetings with Graham and Joseph Lieberman, an independent senator, that "we believe that we had reached" an agreement on the details of a bill.
"But regrettably, external issues have arisen that force us to postpone only temporarily" the senate's work on the bill, he said.
He added that the bill would also expand US nuclear power generation and offshore oil drilling.
The wide-ranging bill aims to reduce smokestack emissions of carbon dioxide and other greenhouse gases associated with global warming.
The proposed legislation already faced an uphill battle in the senate, even before it became enmeshed in a partisan battle between Democrats and Republicans over immigration reform.
"They expect us to do both [climate change and immigration reform] and they will not accept the notion that trying to act on one is an excuse for not acting on the other"
senate majority leader
But with only a few months left before November's congressional elections, senators are trying to determine where their efforts should be focused.
Earlier on Saturday, The Washington Post reported that Graham wrote a letter to his colleagues informing them that unless Democrats stepped back from plans to move ahead with immigration reform rather than the climate change bill, he would drop out of the three-senator working group.
Without Graham on board, efforts to pass climate control legislation could be doomed as he was expected to work to win more Republican support for the bill.
On Saturday Harry Reid, the Democratic senate majority leader, issued a statement that immigration and climate change were both important to Americans.
"They expect us to do both, and they will not accept the notion that trying to act on one is an excuse for not acting on the other," he said.