Siemens Chief Executive Joe Kaeser said Thursday his company is still considering whether to make a bid for France's Alstom SA and would make a decision by June 16, continuing the German company's threat to play spoiler to a proposed $17 billion acquisition by General Electric Co.

Siemens wanted four weeks to examine Alstom's business and financial records as the German company assesses whether to put forward an offer for the French company's power assets, after French government officials asked them to consider a bid.

"So far, we've got everything we wanted," Mr. Kaeser said at an investor conference in New York. "Now we will make up our mind what that means for us."

French government officials courted Siemens after expressing strong reservations about GE's proposal to acquire Alstom's energy assets. Mr. Kaeser didn't tip his hand about whether Siemens would follow through with a formal offer.

GE has made concessions to the French government as it tries to get a deal. It extended its deadline for Alstom to act until June 23. In a meeting with French President François Hollande Wednesday, GE Chief Executive Jeff Immelt pledged to add 1,000 jobs in France, according to a person familiar with the matter.

A Siemens executive told a committee of the French Parliament earlier this week that the company would make a formal bid to create an "alliance" with Alstom.

The Siemens proposal would bring together all of Siemens' railroad rolling stock business with Alstom's transport unit, which manufactures the iconic French TGV high-speed train, said Christophe de Maistre, chief executive of Siemens' French business.

Siemens' proposal, which has yet to be formally presented to Alstom's board of directors, would create a pair of giant European industrial companies out of the existing rival firms--one focused on trains, and the other on energy assets, mainly turbines for coal, gas and nuclear-power plants.

The German company would also consider contributing its railroad signaling business to the new transportation-focused Alstom, Mr. de Maistre said.

Write to Ted Mann at ted.mann@wsj.com

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