* GE offer has improved notably on jobs -president's office
* Shares in Alstom rise 1.9 percent
* Siemens taking time to consider rival offer
(Adds share price, background)
PARIS, May 28 (Reuters) - U.S. conglomerate General Electric has improved its offer for French train and turbine maker Alstom, notably concerning the impact on jobs, an official at French President Francois Hollande's office said on Wednesday.
The comments, which followed a meeting between Hollande and GE Chief Executive Jeff Immelt, signalled a change of tone from Paris. The French government had until now criticized GE's $16.9 billion bid for Alstom's power arm and earlier this month passed a decree giving itself an effective veto on any deal.
On Tuesday evening, Immelt told French lawmakers his group would make detailed commitments to increase jobs in France, including by opening new sites.
He also said GE was considering a tie-up in rail signalling that would give Alstom control of that business, addressing government concerns that a straight sale of the power business would weaken the once-bailed out engineering group by reducing it to its smaller transport arm.
"Today we can see that GE's offer has been detailed, improved, strengthened," said the official at Hollande's office, adding, however, that there was still "some work to be done".
Shares in Alstom jumped as much as 1.9 percent. Alstom management and investors have welcomed GE's bid, saying it would give the company cash to pay its growing debts and the critical mass it lacked in a difficult global power market.
The French government had lately criticized GE's bid and sought to drum up better offers, including from Siemens , Alstom's longtime German rival, which has signalled its interest in making a competing proposal but has yet to make a formal bid.
The chairman of Siemens France said on Tuesday the group hoped to make a formal offer by June 16 to buy most of Alstom's power assets and in exchange give up its own trains business, but that it was still looking at the opportunities and risks of a tie-up. ($1 = 0.7345 Euros)
(Reporting by Julien Ponthus and Natalie Huet; Editing by James Regan)