Siemens entered the battle for French engineering group Alstom on Sunday, after the French government encouraged a European counterbid following a $13bn (£7.7bn) offer last week by the US company General Electric.

The German industrial group said it had written to the Alstom board "to signal its willingness to discuss future strategic opportunities". The surprise move came after the French economy minister, Arnaud Montebourg, made it clear that he would actively seek "other solutions" to the GE bid. He told reporters on Friday that the government "is expressing its patriotic concern and vigilance".

News of the GE move sent shockwaves through France, which fears American control of a big player in the strategic energy sector. Alstom – a direct rival of Siemens – builds high-speed TGV trains as well as power plants. GE was reported last Wednesday to have formally offered $13bn for Alstom's power turbines division, which contributes 70% of Alstom's revenues. The US bid does not involve Alstom's rail division, but the European counterproposal is reportedly designed to create a European energy business around Siemens and a transport group around Alstom.

High-stakes talks between Montebourg and the GE boss, Jeffrey Immelt, were scheduled for Sunday before being delayed on the grounds that the government needed more time to study options in the light of the Siemens approach, and that no hasty decision should be taken. But French analysts said it was doubtful that the government would be able to influence the decision of the Alstom board, which met on Sunday evening.

"General Electric and Alstom have their timeframe, which is that of the shareholders, but the French government has its own, which is that of economic sovereignty," the economy ministry said in a statement. "General Electric and Siemens are two important investors in France, and top-ranking players in our national industrial fabric. The government is prepared to consider their plans, with the concern of preserving the interests of France's industrial base, and to participate financially."

French unions are urging the government to step in again to save Alstom, which was bailed out by the state in 2004 when Siemens was barred from acquiring it. Former industry minister Jean-Pierre Chevènement wrote to the prime minister, Manuel Valls, on Friday to seek his "prompt intervention". Chevènement, who fears that France risks becoming an "amusement park", warned that allowing GE to take over Alstom's energy branch would "deal a fatal blow" to France's nuclear energy sector. Chevènement is senator for Belfort, where both Alstom and GE employ more than 4,200 workers.

It emerged on Sunday that Siemens chief executive Joe Kaeser, in his letter to Alstom boss Patrick Kron, was offering to swap the German group's high-speed trains and locomotives division plus cash – believed to be up to €11bn – in return for the French group's global power assets.

Siemens and Alstom did not comment on the letter's contents on Sunday. But Montebourg appeared to favour the Siemens offer, which he said would create "two European champions in the fields of energy and transport", whereas the GE bid was "a purchase of the energy part of Alstom". However it appears that the Siemens bid resembles an offer from last February that was not taken up by the Alstom board.

The French company's energy division includes turbines for coal, gas and nuclear power, but also windfarms and distribution grid equipment. President François Hollande, who has not yet intervened in the affair, evoked a vision of an "Airbus for energy" at his last press conference in January, referring to the successful Franco-German co-operation in building the European aircraft.

The Alstom takeover battle is an early test of the new government of Valls, a pro-market social democrat who kept the interventionist Montebourg in the cabinet to appease the left wing of the ruling Socialist party.

In his former role as minister for economic recovery, Montebourg blocked the sale of the French version of YouTube, Dailymotion, to the American company Yahoo, last May. Montebourg, whose motto is "Made in France", informed the Indian steel magnate Lakshi Mittal in 2012 that he "was not welcome in France" for wanting to close a plant in eastern France.

Alstom shares were suspended on Friday following the news of GE's takeover bid.