She has accused David Cameron of maintaining a "colonial enclave" in the South Atlantic and taken Argentina's claim to the UN.
But Mrs Kirchner left the summit – attended by North, South and Central American nations – earlier than expected last night as Colombian press reported she was unhappy that a declaration of support for the Argentine claim to the British-controlled territory was not included in the summit's final document, which went unsigned after the USA and Canada used their vetoes.
Mrs Kirchner, to whom the Mercosur trade-bloc and the Union of South American Nations had previously confirmed their support in the diplomatic dispute over the islands, was seeking further backing from the Americas.
During the summit, she said Cartagena was an ideal place to talk about the Falklands since the wall that surrounds the city's historic centre was built by the Spanish crown to protect it from "English pirates".
Mrs Kirchner also reprimanded Juan Manuel Santos, the Colombian president, for failing to mention the islands in his speech.
In his address, Mr Obama maintained the USA's stance of neutrality over the Falklands, saying he wanted to ensure good relations with both Argentina and Britain.
"This is something in which we would not typically intervene," he said, adding that there should be dialogue between the UK and Argentina even though the Coalition refuses to negotiate sovereignty of the Falklands with Mrs Kirchner's government.