The Secretary-General and President Fernández discussed the issue of the Falkland Islands (Malvinas).
The Secretary-General acknowledged the strong regional support for this issue and reiterated that his offices are still keen to work to resolve this dispute, but the parties must be willing to engage.
Delegates are beginning to the gather inside the United Nations in New York for the meeting on the future sovereignty of the Falklands.
Argentine President Christina Kirchner is expected to call for the Falklands to be returned to Argentina.
Islanders have travelled to the UN to assert their right to self determination.
Thirty years to the day after the Falklands war ended, the Argentine President will be ramping up the rhetoric over her country's claim to the islands at the United Nations. Cristina Kirchner's speech will be symbolic, coming on the anniversary of the day hostilities ended.
Our Washington Correspondent Robert Moore reports from the UN in New York.
Islanders, veterans and members of the armed forces marked the 30th anniversary of the liberation of the Falkand Islands today at a service of thanksgiving held at Stanley's Christ Church Cathedral.
Around 400 islanders braved the stormy conditions to pay tribute to their dead.
The war ended on June 14 1982 after Argentinian commander General Mario Menendez surrendered at Stanley.
225 British serviceman, three Falkland Islanders and 655 Argentinian soldiers lost their life in the conflict.
The service was attended by Foreign Officer minister Jeremy Brown.
A group of Falkland Islanders have travelled to the United Nations building in New York to hear President Cristina Fernández de Kirchner argue that the islands should belong to Argentina.
Two members of the islands' Legislative Assembly are hoping to address the UN's decolonisation committee to say they want Argentina to leave them alone. Islander Mike Summer said the committee should put the wishes of the people who live there before the interests of anyone else:
"Their responsibility is not to the United Kingdom or to Argentina. It is to the people of the self-governing British territory."
President Cristina Kircher will lead a delegation of more than 90 diplomats and officials to address the annual meeting of the UN decolonisation committee on the Falklands and 15 other territories. She will be the first head of state to address what is a relatively low-level UN Committee.
She is expected to argue that the islands, known as the Malvinas in Argentina, are still important to the people of Argentina, and that the UK should "stop ignoring" the work of the UN committee and sit down to proper negotiations on their future.
Foreign Office Minister Jeremy Browne has pledged to continue to defend the Falkland Islands from Argentina on the 30th anniversary of the South Atlantic territory's liberation.
The Liberal Democrat MP said: "The Falkland Islands is still a live issue and not just an historical one. We want to make sure that the Argentineans and people right around the world understand that the self determination of the people on the island is sacrosanct.
"They are front and centre stage and we will do what's necessary so they can retain their freedom."
Paratroopers paraded in their hometown of Colchester today to mark the 30th anniversary of the Falklands War.
A drum head service was held at Hollytrees Museum Gardens in Castle Park to commemorate The Parachute Regiments involvement in the 1982 conflict and honour those who were killed in action.
Both 2nd and 3rd Battalions of The Parachute Regiment, then based in Aldershot and Tidworth respectively and now at Colchesters Merville Barracks, played a key role in the British task force sent to successfully repel the Argentine invasion of the Falkland Islands.
Mrs Thatcher's former press officer said the Prime Minister went inside number 10 after making a statement on the night the Falklands ended to MPs, speaking to journalists and greeting members of the public gathered in Whitehall.
Mr Kydd - who was born in Arbroath, Angus, grew up in Edinburgh and lives near Cambridge - said he was left alone with Mrs Thatcher after a clerk handed paperwork to her.
– Ian Kydd, former Downing Street press officer
The two of us were just standing there.
I thought: 'Well, I can't really in circumstances just say goodnight Prime Minister, see you in the morning'.
I thought something a little bit more profound was needed. The best I could come up with was: 'You must be so relieved it is over. It's a special moment'.
I remember her response very well.
She said: 'Yes, Ian, it is. I am relieved I will be able to go to sleep tonight without worrying about those terrible Exocets - and I'm sure Argentine mothers will feel the same'.