She referred to the historic deal as "a ray of sunlight" which she hoped would "warm the hearts of British leaders."
Mrs Kirchner added: "I pray that this action taken by the United States will inspire its European partner".
She also praised the role Pope Francis, an Argentinian, had in the US and Cuba agreement.
The pontiff has previously also backed his home country's sovereignty claim over the Falklands.
The British Foreign Office said there would be no discussions about sovereignty until Falkland Islanders voted in favour of such talks.
A spokesperson said: “There are three parties to this debate, not just two as Argentina likes to pretend.
"The Islanders can’t just be written out of history.
"As such, there can be no negotiations on the sovereignty of the Falkland Islands unless and until the Islanders so wish."