The world's third-biggest advertising agency Publicis has agreed to buy the US digital ad specialist Sapient Corp. for $3.7bn, expanding its digital offering after the failed merger with Omnicom earlier in the year.

The French group is keen to ride the rapid waves of growth in both online advertising and North American advertising, which are booming in comparison with European and traditional advertising.

Publicis' chief executive Maurice Levy has said the failed merger with Omnicon is behind the company's poor performance in recent months.

The proposed $35bn (£22bn, €28bn) merger broke down in May 2014 after executives fell out over how to run the combined companies.

"We've been investing for many years in digital capabilities for one simple reason – it's the future," Levy said, as quoted by Bloomberg. "The pace of innovation is accelerating faster than ever. These mean big challenges for our clients."

Yet, some analysts said the offer of $25 a share was a high price for a company that may have reached its peak growth.

Publicis shares tumbled by as much as 5% in early morning trading and were down 2.6% at 1128 GMT.

Levy said the deal would generate more long-term value than if it were to buy back its own shares instead, saying he provide investors with an update on dividends this month.

"This operation is extremely important for securing the future of Publicis," he said. "It is far better to and deliver a higher growth and higher profits...which will lead to a re-rating, rather than simply buy back our own shares."