Mr Patel said it reflected badly on the Chief Minister, being the head of a state government, to "stoop this low".
"BJP speaking of terrorism?" Mr Patel said in a public meeting in Jambusar. "Congress leaders have suffered the most because of terrorism. We don't need lessons in nationalism from the BJP. They should look into themselves," he said.
"It was unbecoming of a Chief Minister to stoop so low," the Congress leader said.
Congress vice-president Rahul Gandhi also later addressed the public at the same place.
Mr Patel was referring to a suspected ISIS operative arrested by an anti-terrorism squad late last month from Surat, who had earlier worked as a technician at a charitable hospital in Ankleshwar where Mr Patel was a trustee over three years ago.
"I conducted a research. He worked in hospitals instituted by BJP leaders. Care Hospital where he (the ISIS suspect) worked was inaugurated by the Prime Minister," Mr Patel said.