David Cameron raised British concerns about Argentina's increasingly hostile tone towards Britain over the Falkland Islands with Barack Obama at their White House meeting on Wednesday.

The prime minister said that the president reassured him that the US was content with the status quo – that the future of the Falkland Islands will be decided by its population.

Speaking at Ground Zero in New York, the prime minister said: "We discussed the issue briefly yesterday. I wanted to stress how important it is for Britain to set out how clearly we support the right of the Falkland Islanders to determine their own future. They want to remain with us and that is very clear."

The prime minister said that Obama had indicated that he remained unmoved by the tactics of Argentina which is threatening a series of economic measures against the Falklands. Hector Timerman, the Argentinian foreign minister, said on Thursday that Buenos Aires would take legal action any companies involved in oil exploration off the Falklands, according to Reuters.

Cameron said: "The US position is that they support the status quo, they don't argue against the status quo and that is very welcome. They are content with the status quo, they are not challenging the status quo.

"To me it is very important that we stick up for the right of self-determination. The people who live in the Falkland Islands want to continue with their current status.

"What I wanted to do in this 30th anniversary year is send a very clear signal to the rest of the world - Argentina and others - that while the Falkland Islanders want that status Britain will help them keep that status."

The prime minister later acknowledged in a question and answer session at New York university that Britain had been equivocal about the constitutional status of the Falklands 30 years ago. This famously meant that Ronald Reagan adopted an even-handed approach between his two allies – Britain and the junta in Argentina – after the invasion.

Cameron wanted to ensure there would be no repeat of Reagan's initial approach when he made clear that Britain was adamant that the future of the Falklands would be decided according to the principle of self determination – the wishes of its population.

• This article was amended on 20 March 2012. The original referred to an Oval House meeting on Wednesday. This has been corrected.