"At this stage, the commission does not intend to open proceedings in relation to P3 or G6," said Antoine Colombani, commission spokesman for competition policy, according to Reuters.
Marseilles-based CMA CGM also said that the commission had informed it along with fellow P3 members Maersk and the Mediterranean Shipping Co (MSC) that it will not open proceedings in connection with plans to create the network.
But Mr Colombani also told Reuters that the commission will "follow P3 to ensure it remains in compliance with EU competition law".
It is understood that the rival G6 alliance composed of APL, Hapag-Lloyd, Hyundai, MOL, NYK and OOCL has received similar undertakings and cautions.
Said a CMA CGM statement: "P3 partners are pleased. The partners will continue their close cooperation with competition and maritime authorities among others in China and South Korea to explain the nature of P3."
Last June, Maersk, MSC and CMA CGM, announced their intention to establish a long-term operational vessel sharing agreement on the east-west trades, called the P3 Network.
The overall aim with P3 is to make container liner shipping more efficient and improve service quality for the shippers with more frequent and reliable services.
P3, like rival G6 and the CKYHE vessel-sharing agreements, are operational and not a commercial alliances. An independent vessel operating centre will operate vessels independently.
Alliance partners will remain competitors with fully independent sales, marketing and customer service functions and pricing policies.