UPDATE 1-Brazil Vale sees slow recovery in iron ore demand

* Vale sees slow recovery in iron ore demand

* Long-term outlook extremely positive (Adds quotes, details)

RIO DE JANEIRO, June 24 (Reuters) - Demand for iron ore from steel mills is much improved from the extremely depressed level of the fourth quarter of 2008, Brazilian iron ore miner Vale (VALE.N: Quote, Profile, Research)(VALE5.SA: Quote, Profile, Research) said on Wednesday, but the company expects a "slow recovery".

"We are living through a crisis that we seem to be coming out of," Fabio Barbosa, Vale's financial director, added during a seminar in Rio de Janeiro. "There will be repercussions but our confidence in the future remains, due to an extremely positive outlook in the long term."

Vale is recovering from a sharp drop in demand for iron ore from steel mills after the global financial crisis deepened in late 2008.

Barbosa said that demand for ore from steel companies was "much improved" from the fourth quarter but added that "the recovery should be slow."

Vale, the world's largest producer of iron ore, is in the midst of critical annual price negotiations with Chinese steel mills, which are demanding at least a 40 percent reduction in the price of ore from 2008 levels.

"We have important signals that there is a dismantling of the systemic risks to the North American financial system, but there are still uncertainties," he said. (Reporting by Denise Luna; Writing by Reese Ewing; Editing by David Gregorio)