Argentina, Brazil and Paraguay have denied terrorists are operating in the area where their borders meet, after a fresh anti-terror move by the US.
The US said those targeted by sanctions were aiding Hezbollah
On Wednesday the US Treasury froze the assets of nine people and two companies alleged to have transferred millions of dollars through the "Triple Frontier".
The US said members of Hezbollah were engaged in illegal activites there.
But the South American nations said Washington had not provided any "new information" to support the claims.
The so-called Triple Frontier has a reputation as a centre for drug trafficking and money laundering.
The US Treasury alleged that those targeted by its sanctions had provided financial aid to a "specially designated global terrorist" named Assad Ahmad Barakat, who has been cited for his support of the Hezbollah leadership.
"Assad Ahmad Barakat's network in the Tri-Border Area is a major financial artery to Hezbollah in Lebanon," said Adam Szubin, director of the Treasury's Office of Foreign Assets Control.
"[This] action aims to disrupt this channel and to further unravel Barakat's financial network."