By Karolina Tagaris
ATHENS, Jan 24 (Reuters) - A migrant boat mishap that killed at least two and left 10 missing has become the latest headache for Greece's government, which had to deny claims its coast guard triggered it by towing the boat toward Turkish waters.
Migrant drownings are not uncommon in Greece, a major gateway into the European Union, but the latest incident has drawn attention over allegations that Greece breached EU law by trying to push the 28 migrants back to Turkey.
Greek prosecutors in the Dodecanese islands began an inquiry after the U.N's refugee agency UNHCR, rights groups and political parties including Prime Minister Antonis Samaras's own coalition partner PASOK sought an inquiry into how the deaths occurred while the coast guard was rescuing the boat.
The vessel capsized as it was being towed. The coast guard says it was headed to Greek waters but survivors told the UNHCR they thought they were being towed towards Turkey.
Samaras has made illegal immigration a priority for his government and Greece's rotating six-month EU presidency. Greece has long complained of being overwhelmed by migrants and its economic crisis has boosted anti-immigrant sentiment.
Criticism of the government's handling grew after television footage showed survivors arriving at the port of Piraeus near Athens on Thursday, recounting in tears how they watched their children drown while coast guard officials looked on.
"My one-year-old child was screaming 'Mom, dad, help,'" said one of the survivors, who said his wife and three children were missing and broke down in sobs.
"Twelve drowned and the minister couldn't care less", the leftist newspaper Eleftherotypia wrote on its front page.
Amnesty International said the incident pointed to "a blatant disregard for human life shown by the Greek coast guard" and leftists and human rights' groups, which accused the coast guard of murder, have called for protests in the coming days.
"The loss of human life at sea is something our seafaring people will not accept," said Mikas Iatridis, a lawmaker from the right-wing Independent Greeks party.
Greece's maritime affairs minister, who angered many earlier this week for saying Greece's borders were "not an unfenced field for whoever wants to enter," said on Friday that Greece was meeting its international obligations.
"The orders are clear: first to safeguard sea borders and second that we cannot and must not suffer any loss of life at sea," Miltiadis Varvitsiotis said. "Each loss of life is a huge loss for us."
(Reporting by Karolina Tagaris; Editing by Tom Heneghan)