* Migrants were rescued off Libya in early August
* Six states have offered to take them in
* Far-right Salvini at odds with prime minister
* Says doesn't trust the offers of relocation (Adds kidnapping case opening)
By Guglielmo Mangiapane
LAMPEDUSA, Italy, Aug 16 (Reuters) - A charity rescue ship carrying 134 migrants, mostly Africans, was stranded off the coast of Italy on Friday as a political battle in Rome stopped it from docking and even the medical conditions of those on board were disputed.
The migrants, picked up off Libya over the last two weeks, are waiting to disembark on the southern Italian island of Lampedusa, but far-right Interior Minister Matteo Salvini has ordered his officials not to let them do so.
Salvini, who has built his popularity on a vigorous campaign against illegal immigration, is acting in defiance of his own prime minister and despite six European Union nations agreeing to take the migrants in.
Their plight underlines the breakdown of Italy's ruling coalition and how immigration has become central to Salvini's plan to take his right-wing League party out of government, drag the nation to elections and return to power as prime minister.
Separately, the prosecutor's office told Reuters on Friday that a Sicilian prosecutor has opened an investigation for kidnapping, though it was not clear who the subject of the probe was. Last year an Italian court tried to put Salvini under investigation using the same motive, but parliament blocked the move.
France, Germany, Romania, Portugal, Spain and Luxembourg have said they will help relocate the migrants, but the reaction from Salvini's interior ministry was sceptical.
"It is not clear that the other countries are willing," a ministry spokesman said.
The health of the migrants on board was the subject of a dispute between the Salvini and the Spanish charity group Open Arms, which runs the rescue boat of the same name, as European institutions also got involved.
Thirteen people, who Open Arms said were seriously traumatised or requiring medical attention, were moved off the boat on Thursday.
"They are self-harming and getting angry with other people in the group," Alessandro di Benedetto, a psychologist with Italian aid group Emergency, told RAI radio after examining five of those brought ashore.
"Some of them are having suicidal thoughts, so they think it is better to die here than go back there," he added.
However, Salvini cited the head of Lampedusa's hospital who examined the 13 evacuees as saying that one of them had an ear infection, while all the others were fine.
"We have the umpteenth mockery by the Spanish NGO running the Spanish ship which has been cruising the Mediterranean with the only aim of collecting as many people as possible to bring them always and only to Italy," Salvini said in a statement.
"In all this time they could have gone to a Spanish port and come back three times," he added.
The president of the European Parliament, David Sassoli, said he hoped "the Italian authorities understand the gravity and the humanitarian emergency aboard the boat and allow it to enter the port today."
Salvini's tough anti-immigration rhetoric has helped boost his popularity at the expense of coalition partners the 5-Star Movement, but his surprise bid to bring down the government and call an election is running into trouble.
On Friday, he tweeted a picture of himself gazing upwards and the message: "Timidity? Appeals to false notions of compassion? Open ports? Thousands of arrivals? Not in my name! Italy, hold your head up high again!"
In Brussels, a European Commission spokeswoman said the EU welcomed the other countries' cooperation and was ready to give operational support once a solution was found for landing the rescued migrants.
LAND IN SIGHT
Salvini argues that Italy, which lies close to the Libyan coast, should no longer be the main gateway for migrants fleeing Africa for Europe. He accuses the charities of becoming "taxis" for people-smuggling gangs.
Prime Minister Giuseppe Conte, who belongs to no political party but is close to 5-Star, accused Salvini of exploiting the issue.
This standoff is the latest in a series that have seen charity boats caught up in European political tussles over the past year, drifting at sea as states argue over who is responsible for opening their ports.
"We are living an unbearable agony on board," Open Arms said on Twitter, posting a video of people lying close together on the deck, swaddled in blankets.
"Land in sight and no solution. The rights of 134 people are being violated with every passing minute. If European politicians are incapable of setting limits, what do we have left?"
Citizens of Eritrea, Somalia, Nigeria and Cameroon are among those on board, a spokeswoman for Open Arms said.
The Open Arms boat was allowed into Italian waters on Thursday after an administrative court in Rome overruled a ban on its entering that Salvini had previously imposed. (Reporting by Guglielmo Mangiapane; Additional reporting by Wladimir Pantaleone in Palermo, Alexandra Regida in Brussels, Isla Binnie in Milan, and Ingrid Melander in Madrid; Writing by Isla Binnie and Gavin Jones; Editing by Mark Bendeich, Angus MacSwan and Toby Chopra)
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