The decision was made to allow ongoing discussions with the government to continue. The original deadline was 2 June.
GE says it views the extension "positively" and said ongoing talks remain constructive.
The US-based company made the bid for Alstom's power business at the end of April but it was faced with reticence by President François Hollande's government, which has called on GE to improve its offer.
Siemens is also considering making a counter-bid for the business and could table an offer in the next few days.
Earlier this week, GE said it would be willing to sell Alstom's wind division to French investors if the American firm succeeded in taking over the energy business.
French turbine manufacturer Areva has expressed an interest in taking over Alstom's wind division.