Procter & Gamble declared victory Tuesday over activist investor Nelson Peltz, saying initial figures show it won the biggest proxy battle in history. But the narrow win puts pressure on the owner of Bounty and Tide to move faster in its turnaround and regain the support of investors.

"The preliminary proxy results are ones I'm pleased with," said CEO David Taylor on CNBC. "I know from talking to many investors, they support the strategy. Do they want to see us move faster — I'm sure — and we're moving faster."

P&G will file results with the Securities and Exchange Commission when the vote is finalized.

Trian has already said it plans to challenge the proxy results. Peltz added in an interview with CNBC that regardless of the outcome he will continue to advocate for the company to follow his recommendations, which include streamlining its structure and small acquisitions of innovative brands.

"I don't think they're serving their shareholders properly. I don't think they have a structure today that's right for that business," Peltz said.

Peltz's fund Trian Partners revealed a roughly $3.5 billion stake in P&G in February and in June nominated him for a board seat.

P&G shares closed Tuesday down less than 1 percent.

The consumer goods giant has for years struggled with market share as sales have slowed and it faces competition from more innovative or upstart brands. Under Taylor, who joined as CEO in 2015, the company simplified its corporate structure, streamlined its portfolio, poured more money into research and development and worked to improve operations.

Since Taylor took the reins, P&G's stock has outpaced most U.S. consumer products companies, including Clorox and Colgate-Palmolive, though it underperformed against the