An agreement on the principle at least of a state visit was struck at talks between Mr Major and President Menem in New York on the fringes of the 50th-anniversary celebrations of the United Nations. It was the first summit-level meeting between the countries since the Falklands war.
British officials said Mr Major made the offer on condition that a recent thaw in ties continues and specifically that proposals to agree a fisheries agreement are successfully carried through. Mr Menem suggested in return that Mr Major could visit Buenos Aires. The Argentine Foreign Minister, Guido di Tella, said Mr Major and Mr Menem agreed to meet again in Madrid before the end of the year. Both men declined to give interviews after their meeting. Diplomatic ties were restored in 1990, shortly after Mr Menem came to power.
Even until recently, British officials have indicated that the idea of an official visit by the Argentine president was still unthinkable.
Part of the change in atmosphere has arisen from the signing last month of an oil-exploration agreement, under which Buenos Aires agreed not to interfere with the licensing by Britain of companies wishing to search for oil in Falkland Island waters.
There was no direct exchange between the two leaders yesterday on the core issue of the sovereignty of the Falklands, known in Argentina as the Malvinas.
Mr Major told reporters in New York that Britain's position on retaining them as British territory remained "unshakeable". A British source said last night: "What we're concerned with here is steadily to see whether it is possible to improve relations. We believe that what people want to see is Britain preserving sovereignty over the Falkland Islands in an environment where the threat of war from Argentina is removed."
Earlier, Mr Menem had signalled that he expected the fisheries pact, which will focus especially on conserving stocks of squid in the South Atlantic, to be signed "towards the end of this year or early next year".
Mr Menem was at pains to emphasise how far his country's relations with Britain have improved since diplomatic ties were restored.
"Our relations with the UK are good," he insisted. He said that trade between the countries was improving and noted, as an example, that British Airways is now flying to Buenos Aires. The Argentine President, who has vowed before domestic audiences to restore the Falkland Islands to his country by the year 2000, conceded that he had no plans to raise the issue directly with Mr Major. "As you know, sovereignty has been placed under an umbrella for the time being," he said before the meeting.
Britain took over the Falklands, located in the South Atlantic, in 1833. Argentina invaded the islands in 1982, triggering a 74-day war in which Britain regained the islands.