* Talks on overhauling labour rules enter final stretch
* Employers to discuss key union demand -union negotiator (Adds talks adjourned, to resume on Friday)
By Nicholas Vinocur and Yann Le Guernigou
PARIS, Jan 10 (Reuters) - French employers offered some concessions at a fresh round of talks to overhaul labour rules on Thursday but stopped short of ceding to union demands to raise welfare charges on short-term job contracts, union officials said.
The negotiations - a test bed for Socialist President Francois Hollande's chances of enacting reforms in areas past governments have shied away from - packed up for the day late in the evening with no deal and were due to restart on Friday.
Hollande, battling stalled growth and rampant unemployment, has called on business leaders and unions to strike a "historic deal" to overhaul the labour market to help firms adjust their wage burden in a downturn and give workers more job security.
He is pressing the parties to conclude a deal by Jan. 15 but says he will introduce draft new labour legislation in the first quarter of 2013 regardless of whether a deal is struck.
As talks restarted on Thursday after an end-of-year break, union officials said employers were ready to discuss their demand to increase welfare charges on short-term contracts.
By the evening, however, revisions to their position ceded some ground on long-term contract conditions but did not include concessions on the thornier issue of short-term contracts, CFTC union official Joseph Thouvenel said.
"This cannot be the definitive version because there is nothing on short-term contracts," he told reporters.
An employers' group representing very small companies said it would not sign the proposed accord in its current form.
Hollande, saddled with dismal approval ratings eight months into his term, told reporters in southwest France he was confident the unions would seize the opportunity to strike a deal.
Without support from unions and employers, any law could face street protests and unions could push left-wing lawmakers to water it down.
The previous round of talks broke up without an accord and both sides accusing the other of making unacceptable demands.
Laurence Parisot, head of the Medef employers union, told a morning show on Europe 1 radio that only a deal that put France on par with "the highest international standards in terms of flexi-security" would be acceptable.
Flexi-security refers to a cooperative approach to labour relations widely used in northern Europe in which employees accept a degree of flexibility in working arrangements in return for employer commitments on job security.
France wants to emulate that to address high unemployment and to eradicate the split in its job market between inflexible permanent contracts and short-term contracts increasingly used by employers but which offer workers little or no job security.
Jobless claims are at a 15-year high with an unemployment rate above 10 percent.
Parisot said the Medef and its negotiating partner, the CGPME small- and medium-sized business group, would consider giving unions a voice and votes on company boards, and favoured making complementary health benefits automatic for workers.
Parisot repeated her employers' union's refusal to impose higher welfare charges on short-term contracts. But a negotiator for the moderate CFDT union, France's largest by membership, said Medef was now willing to discuss them.
"They (Medef) said they had understood that the issue of short-term contracts was unavoidable and that we would be discussing them today," said Patrick Pierron, adding that use of contracts of less than a month had exploded in the past year.
But, he added: "I think it's optimistic to think that it (the talks) will be over this evening."
Unions say they could accept in-house deals allowing firms to temporarily cut work hours during downturns, similar to arrangements in Germany.
But even the moderate CFDT and CFTC unions remain opposed to the creation of new long-term job contracts that incorporate periods of lower pay and shorter working hours.
Bernard Thibault, head of the hardline CGT union, said his group would not sign any deal in favour of de-regulation.
"What I can tell you is there is no way the CGT will approve the spirit of proposals from management's camp." (Additional reporting by Jean-Baptiste Vey; Editing by Ron Askew/Mark Heinrich)