(Removes typo in headline)
* Demand recognition of their language, more say in constitution
* Impact of closure on Italy gas supply visible on Tuesday
* Protestor already shut oil port
TRIPOLI, Nov 11 (Reuters) - Protesters have shut Libya's gas export pipeline to Italy, its only customer, demanding more rights for the Amazigh, or Berber, minority.
Although the closure on Monday of the Greenstream pipeline will take several hours to register at the other end, it adds to Italy's energy headaches after Ukraine halted gas imports from Russia, which could also impact supplies. Italy depends heavily on Russian gas.
Amazigh protesters last month seized the port at the Mellitah complex, some 100 km west of Tripoli, and have already shut down oil exports from there.
The port is operated by Libya's National Oil Corp and Italian energy company Eni.
"We tried to convince them not to close the pipeline, but it's closed now," Munir Abu Saud, head of the local oil workers' union, told Reuters.
"Sadly, its true," said a senior official at the Libyan oil ministry. Tripoli has seen its authority crumbling over its restive regions and fears an exodus of foreign oil companies and investment.
The Amazigh minority in September shut a pipeline feeding gas from Eni's Wafa field to export facilities at Mellitah. Although this squeezed exports, much of the gas Libya sends to Italy comes from offshore fields.
Gas flows on Greenstream were at 15.9 million cubic metres on Monday - for now the same amount requested by operators, data from gas grid operator Snam showed.
"At the moment we do not see supply problems for Italy," said Eni, the biggest oil and gas operator in Libya, in an email response.
Exports from Africa's fourth-largest gas reserve holder to Italy have fallen since last year as production rates lag pre-civil war levels.
Libya's 9.9 billion cubic metre/year Greenstream can meet up to 12.2 percent of Italy's annual gas demand, although last year it accounted for just nine percent of imports, a share that has continued to drop this year.
Italy is 90.4 percent dependent on imports for its gas needs, with a clear majority coming from Russia - of 31 percent in 2012, though that share has likely grown this year.
A spokesman for the protesters camped out at the Mellitah complex said they had ordered the closure because Libya's parliament and the government had not met their demands by Sunday.
"This time it is for real because the General National Congress did not meet our demands," the spokesman said.
The Amazigh protesters want their language guaranteed under Libya's planned new constitution and a bigger say in a committee to be elected to draft the constitution.
The GNC debated the issue on Sunday but has not yet found a solution, said GNC Spokesman Omar Humeidan.
Two years on from the 2011 overthrow of Libyan leader Muammar Gaddafi the country remains beset by violence, strikes and protests over political rights, jobs, and how its oil wealth is to be shared.
Most ports in eastern Libya are shut though the government had managed to end blockages of western ports in September.
(Reporting by Ghaith Shennib, Ulf Laessing, Stephen Jewkes in Milan, Oleg Vukmanovic and Lin Noueihed in London; editing by William Hardy)