So far this year, there's been $217 billion in M&A activity in the U.S., according to Dealogic. That's the fastest start since 2000 and more than double the amount tallied in the comparable year-to-date period of 2012.
Mergers and acquisitions are "just getting rolling," Peltz predicted. "I think there are many more deals coming."
Explaining his reasoning, Peltz said, "Revenue growth is hard to come by. I think most of Corporate America feels that they have skinnied down their operations to a point where they can't get much more out of it. So synergies are the next wave of getting [earnings per share] growth."
He said that he had acted on this belief. "We bought Lazard because we thought the M&A market was coming back and it has."
(Flashback: Trian's Peltz: Confident in Lazard Stock)
Peltz's Trian Fund Management disclosed last summer the purchase of a 5.1 percent stake in the investment bank.
—By CNBC's Matthew J. Belvedere; Follow him on Twitter