* Offer presented to Gemalto board on Nov. 28
Bid represents 42 pct premium on last closing price
* Gemalto's biggest shareholder Bpifrance backs bid -Atos CEO
By Mathieu Rosemain and Cyril Altmeyer
PARIS, Dec 11 (Reuters) - French technology consulting firm Atos offered to buy Gemalto for 4.3 billion euros ($5.06 billion) on Monday to boost its cyber security services as states and big corporations seek to cope with a growing number of attacks on the Internet worldwide.
The bid comes as Gemalto, the world's largest maker of chips found in mobile phones and credit cards, is under pressure after posting four profit warnings in a year and having missed a chance to strengthen its security business through a large acquisition.
The combination would strengthen Atos in the burgeoning so-called Internet of Things (IoT) sector of internet-connected machinery and household devices able to collect and exchange data using embedded sensors and European payment services on top of digital security, it said.
Atos said it delivered an offer to Gemalto's board on Nov. 28.
Shortly after issuing the formal offer, Atos Chief Executive Thierry Breton said he had already received the backing of Gemalto's biggest shareholder, France's state-owned investment bank Bpifrance.
"I've met the main shareholders and Bpi in particular," Breton said in a call with reporters following the announcement of the unsolicited bid for Gemalto.
"Bpi is not only favorable to this operation of European consolidation, but it also authorized me to tell you about it," he added.
Bpifrance holds 8.51 percent of Gemalto's shares, according to the group's last annual report. Gemalto and Bpifrance were not immediately reachable for comment.
Gemalto had to postpone to March 2018 the presentation the presentation of its next multiyear strategic plan, after several profit warnings notably caused by slowing demand for credit card chips.
The group's shares have shed 38 percent so far this year compared with an increase of 24 percent for Atos.
Since Breton took the helm of Atos in November 2008, the firm has multiplied its stock price by close to six times, outperforming French rival Capgemini and U.S. companies Accenture and IBM.
Atos' revenue has more than doubled over the period to reach 11.7 billion euros in 2016, after having bought assets from Germany's Siemens, U.S. group Xerox and France-based computer company Bull.
Gemalto had sales of 3.2 billion euros in 2016.
The all-cash bid reflects a price of 46 euros per Gemalto share, representing a 42 percent premium on the group's last closing price, Atos said in a statement.
The bid would be financed by Atos' existing cash resources and debt, the company said without elaborating.
Breton said that two banks had already given their approval for a potential loan. ($1 = 0.8495 euros) (Editing by G Crosse)