Siemens and Mitsubishi unveiled late on Monday a joint bid that valued Alstom's energy division at €14.2 billion ($19.2 billion) - €2.0 billion more than US giant General Electric.
Siemens chief executive Joe Kaeser said on Tuesday their joint bid was the more competitive following a meeting with French President Francois Hollande.
The deal would also see Mitsubishi Heavy Industries take a 10 percent stake in Alstom, and the company's chief executive Shunichi Miyanaga said they would like the French state to match or exceed that.
GE has made a firm offer of €12.35 billion to buy the power division of Alstom, which accounts for about 70 percent of its activities. It expires on Monday.
The US-based group responded swiftly to the Siemens-MHI offer on Monday by saying it would not engage in a bidding war, however a source close to the deal said GE was working behind the scenes to make its offer more attractive.
GE is considering the possibility of creating a joint venture in transport with Alstom and, similar to MHI's proposal, an industrial alliance in steam turbines, the source said.
Alstom, which builds power-generation systems and railway equipment, including the TGV high-speed train, says it is not strong enough in the world market for power stations and it is suffering from weak demand in Europe.
'European rail champion'
When the advanced state of negotiations by the Alstom board to sell the power division to GE became known, the French government objected, fearing a loss of jobs and influence over a company which also makes turbines for nuclear reactors.
Paris encouraged a counter-offer by Siemens, which has huge power interests and also has big rail activities, and has been seeking to obtain the best deal possible for the struggling firm.
Under the terms unveiled Monday, Siemens offered to pay €3.9 billion for Alstom's gas turbine business, and in a nod to the government's interests, the president of Siemens' supervisory board Gehrard Cromme said on Tuesday it would create a European "champion" in railway equipment by forming a joint operation headed by Alstom.
MHI would buy from French conglomerate Bouygues a stake of up to 10 percent of Alstom, and create three joint businesses in steam turbines, hydraulic turbines, and electricity networks in which it would hold minority stakes.
The Japanese company would also inject 3.1 billion euros in cash.
Mitsubishi's Miyanaga told French lawmakers on Tuesday that "we strongly wish to have the State contribute to purchase of Bouygues' stake so the company remains French."
French officials have not expressed publicly any desire to become a shareholder in Alstom, but a source close to the negotiations told AFP it has considered doing so via a state investment bank.
Bouygues had said after the closing of stock trading on Monday that it was not interested in selling Alstom shares.
Analysts said the German-Japanese offer was too complex and would break up Alstom.
The GE bid had the merit of being "clear and coherent," said analysts at brokerage Aurel BGC commented.
"MHI-Siemens offer has been conceived to seduce the government and not the French group. We are sceptical.
"MHI would not contribute assets and is proposing a complex solution which would result in the Japanese company holding different stakes in various activities of the energy division, while remaining a competitor to Alstom."
Shares in Alstom fell 1.24 percent to close at €28.97, compared to an overall rise of 0.58 percent for France's main stock index.
Jeal-Luc Gaffard, director of the French Economic Observatory (OFCE), expressed concern about the government playing too great a role in business deals.
"What was done in the past was not a great success. Politicians are not the best to judge the relevance of industrial processes," he added.