David Cameron and Spanish PM Mariano Rajoy eventually agreed not to let the overseas British territory get in the way of their cooperation over other key issues during talks in Brussels to try to end the diplomatic spat.
Garcia-Margallo linked the Falklands and Gibraltar earlier this month by comparing Spain's battle to get Britain to surrender sovereignty over the Rock with Argentina's demand for control of the Falklands.
He said during a trip to Argentina's neighbour Uruguay: "The similarities are enormous" and insisted both Gibraltar and the Falklands were in need of "decolonisation."
It was not clear last night whether Spain was refuting any agreement at all with Argentina - or was just annoyed about the timing of the announcement by Buenos Aires.
The Argentine foreign ministry, in the statement posted on its website yesterday said: "Hector Timerman and Spanish counterpart Jose Maria Margallo met in New York at the margins of the UN General Assembly to discuss bilateral agenda issues.
"In particular they discussed the common ground regarding sovereignty disputes over the Falklands and Gibraltar.
"They agreed on joint measures to press Great Britain to comply with the mandate from the United Nations to dialogue."
Several newspapers around the world including the Wall Street Journal compounded the embarrassing Argentine error on the Spanish foreign minister's name by printing their version instead of the correct name Jose Manuel Garcia-Margallo.
A Spanish Foreign Office official confirmed it was a mistake - although it remained uncorrected this afternoon.
Spain has blown hot and cold over supporting Argentina's long-standing claim to the Falklands.
Jesus Gracia, its secretary of state for Ibero-America, insisted last year during a visit to Argentina Spain backed its claim.
But Spain described a dispute between Britain and Argentina over oil exploration off the Falklands as a "bilateral issue" when tempers flared two years ago.
Spain's relationship with Argentina took a battering when its president Christina Kirchner nationalised oil company YPF, a subsidiary of Spanish firm Repsol, in April last year.
Argentina seized the Falklands by force in April 1982 but were expelled by UK troops in a 74-day war, costing the lives of 258 British servicemen and 649 Argentinians.
Argentine président Christina Kirchner has made regular verbal attacks on Britain over the Falklands.
But since taking power after the death of her ex-president husband, she has insisted peace and diplomacy are the only way forward while attempting to get regional backing for her country's sovereignty claim and press the issue at UN meetings.