The wives, girlfriends and relatives of the six Britons launched the online petition titled "Help Free the 6 British Ex-Soldiers from Indian Prison" and called on Foreign Secretary William Hague to help the men.
The Foreign and Commonwealth Office confirmed the detention of the six men and a spokesperson said it was providing consular assistance. "We are in touch with the local authorities," the spokesperson said.
"They should not be there. It is not them at fault," Yvonne MacHugh, the girlfriend of one the sailors, told The Times.
The former soldiers work for AdvanFort, an American company that provides security guards to protect ships from pirates.
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They were resting on MV Seaman Ohio, an American-owned support vessel, with 19 other guards from different countries and 10 crew members, waiting for their next mission.
The men allegedly ran into problems with the Indian authorities while trying to avoid a typhoon that was sweeping through the region, according to family members.
A spokesman for AdvanFort said the allegations were "without merit". He said: "It is common practice to purchase small quantities of fuel in emergencies, and AdvanFort provided all necessary documentation and certifications to the Indian authorities."
No one has been charged so far.