Kevin and Alison Hill have hinted they may sue the government department over misinformation given to them about the death of their daughter, Laura.
The Foreign Office originally told the couple the 25-year-old dental nurse had been found dead on
a park bench in Buenos Aires last October and had died from natural causes.
But two months later it was revealed she had been found in an apartment building with extensive bruising on her body and had possibly taken a lethal dose of cocaine.
The family say had they known their daughter's death was suspicious, they would have flown to Argentina immediately.
"We have been constantly misinformed and the Foreign Office has got to take some responsibility for that," said Mr Hill at a press conference at the Chatsworth Hotel in Eastbourne on Friday.
The family was also given fresh hope on Friday when an Argentinian journalist told them the prosecutor in Buenos Aires would re-open the investigation in to Laura's death.
Maria Laura Avignolo, from the country's national newspaper Clarin, said she had managed to uncover some details surrounding Laura's death and the authorities were willing to provide them with all the information the Foreign Office had been unable to.
Mrs Hill said, "We have been given information by the Argentinian journalist today which we have been trying to get through the Foreign Office for 10 months.
"It is a shock but it has given us fresh hope that we may find out exactly what happened to Laura."
The Hills' case has been taken up by Eastbourne MP Nigel Waterson, who said he would now like to see the Argentinian authorities invite officers from Sussex Police to Buenos Aires to help with any re-investigation.
Mr and Mrs Hill said they had nothing but praise for officers who had been investigating on behalf of the coroner.
Detective Chief Inspector Trevor Bowles from the Major Crime Branch said, "Sussex Police has provided a family liaison officer to Mr and Mrs Hill since the tragic death of their daughter Laura, in Argentina in October 2007.
"We have had a positive and constructive relationship with Mr and Mrs Hill and that continues to this day. The role of Sussex Police has never been one of investigating how Laura died in Argentina but rather to conduct local enquiries on behalf of the East Sussex Coroner Alan Craze in order that he may be able to hold an inquest at a later date."
The Hills have vowed to continue their search for the truth into Laura's death and on Friday they were offered return air tickets to Buenos Aires by Eastbourne businessman Sheikh Abid Gulzar, who owns the Chatsworth Hotel.
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