* Tripoli government invited Italy into its waters
* Some 600,000 boat migrants have come to Italy since 2014
* Mission hinges on parliamentary support
* Libya Presidential Council denies permission given (Adds Tripoli denial)
By Steve Scherer
ROME, July 27 (Reuters) - Italy intends to deploy several ships in Libyan waters by the end of August to combat human trafficking and stem a huge influx of immigrants, a government source said on Thursday.
A mission plan should be brought to the Cabinet for approval on Friday, and the necessary parliamentary vote to endorse it may be held next week, the source said.
"The exact number of ships and sailors is still being worked out," said the source. If parliament approves, the mission might begin by the end of August, he said.
Amid mixed signals from Tripoli over whether Libya would allow the deployment, Prime Minister Paolo Gentiloni met with military chiefs and ministers on Thursday to discuss "security, immigration and the Libyan situation", according to a statement.
Some 600,000 migrants have reached Italy by sea from North Africa since 2014, making immigration a potent political issue and putting the country under increasing pressure to manage the new arrivals.
Most have embarked from Libya, where people smugglers operate with impunity in the turmoil that has gripped the country since the fall of Muammar Gaddafi in 2011.
Gentiloni told reporters the mission was "a possible turning point".
Details of the plan will be presented to parliament on Tuesday, he said.
In a letter sent on Sunday that Gentiloni outlined on Wednesday, Libya's U.N.-backed government in Tripoli invited Italian warships into its territorial waters. Libyan Prime Minister Fayez al-Serraj was in Italy for the announcement of the plan on Wednesday.
On Thursday, Gentiloni said he had spoken to several European "colleagues" who supported the mission. "It pleases me to know there is a lot of support in Europe to this new possibility," he said.
Despite Serraj's visit, Libya's presidential council in Tripoli on Thursday denied it had given permission for Italian forces to be in Libyan waters and warned sovereignty was a red line.
"What was agreed with Italy was the completion of the programme supporting the coast guards to train and prepare them with armed capabilities and equipment for saving lives of migrants, and to confront criminal organizations," it said.
"....National sovereignty is a red line that cannot be passed."
The council gave no explanation for the conflicting positions. But Libya's U.N.-backed presidential council is split and Serraj has struggled in a country where rival factions have steadily battled for control since Gaddafi's fall.
In the past, officials have backtracked on statements that appear to impact Libya's sovereignty, such as counter-terrorism cooperation, as they come under pressure from rivals at home.
Tripoli had in the past refused access to its waters to the European Union's anti-trafficking sea mission Sophia since 2015, hobbling efforts to stop smugglers.
COMMAND SHIP
A command ship heading a flotilla of at least five smaller vessels and up to 1,000 sailors will be used in the mission, newspaper Corriere della Sera reported on Thursday. Planes, helicopters and drones will also be used, it said.
The rules of engagement, the area of coastline to be patrolled and the nature of cooperation with Libya's security forces have yet to be defined, the source said.
One thing is clear: Italy wants migrants picked up by its ships - should the Libyan coastguard not be able to intervene directly - to be returned to Libya and not taken to Italy.
"This all makes sense only if we can limit the arrival of migrants in Italy," the source said.
Migrants who reach international waters are brought to Italy because Libya is not considered safe for refugees, and returning them there would be a violation of international non-refoulement law .
Because the Libyan coastguard returns migrants to detention centres where they are held indefinitely in "inhuman" conditions, according to the United Nations, Italy wants U.N. agencies to bolster their presence there and to operate migrant camps that respect human rights, the source said. (Additional reporting by Ahmed Elumami in Tripoli, editing by Larry King and John Stonestreet)
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