Islanders show little sign of wanting to change flag
But he said the islands will be won from Britain by using patience and perseverance rather than force.
At Tuesday's memorial ceremony in Argentina's far south, President Duhalde told a gathering of war veterans that the islands are undeniably Argentine.
Few have good memories of 2 April 1982 - when hundreds of Argentine commandos arrived in the island's main town of Stanley, at the start of the 10-week war with Britain.
'Not in vain'
"The Malvinas are Argentina's" went the song that floated across the gathering of 1,200 war veterans in Ushuaia, on the southern tip of Argentina.
The patriotic song, referring to the Falkland Islands by their Spanish name of Las Malvinas, concluded Tuesday's ceremony.
It was held exactly 20 years after the first Argentine troops arrived in Ushuaia - when the town was used as a staging post for the original invasion.
The BBC's correspondent Peter Greste says the veterans came with medals, flags and war mementos - not just to remember their comrades who died but to assert that while the invasion strategy may have been fatally flawed, their cause was still just.
President Eduardo Duhalde told his audience that their fight would not be in vain.
"The Malvinas are ours and we'll get them back," he said. "Not with wars but in the manner Argentines use to recover their things - with faith, patience and perseverance."
Quiet reflection
In the Falkland Islands, though, the atmosphere was very different.
"It's a moment for reflection, certainly not celebration, that's for sure," said former teacher Phyl Rendell.
"It's hard to believe these 20 years have gone by. It has been 20 years of trying to make the sacrifice of those who died worth it."
Britain and Argentina have long disputed sovereignty over the Falkland Islands, which are situated 350 miles (550 kilometres) from Argentina, but are populated almost entirely by people of British descent.
Twenty years on, the island's residents have not changed their views.
"The attitude to Argentina is if they drop their claim then they are welcome - but until they understand that these islands won't belong to them, they won't get anywhere," said shopkeeper Paul Howe.
The Governor of the Falklands, Donald Lamont, said it will take time for people to be relaxed about Argentina.
"The breach of trust was pretty definitive. It's ingrained," he said.
He added that Britain remained "committed to the right of self determination for the islanders, and has made it clear that sovereignty is not for negotiation".
Despite the continuing debate, there was little bitterness towards Britain during the Argentine celebrations, our correspondent says.
Most of the anger was reserved for Argentina's military government who originally ordered the catastrophic invasion.