Kirchner, whose centre-left government is mired in a bitter US court battle with what it terms "vulture fund" creditors, met privately with her compatriot for 15 minutes before they exchanged gifts and lunched together at the Casa Santa Marta, the pope's residence.
"The pope received me with the same warmth as always," Kirchner told journalists after what was her fourth meeting with the 77-year-old pontiff.
The meeting was seen as a sign of support for the Argentine leader, invited personally by the pope just days before she addresses the United Nations General Assembly in a bid to tackle creditor sharks.
Kirchner had hoped to get a sympathetic ear for her calls for global reform to stop speculative creditors from buying up struggling countries' bonds then suing them for full payment, thus blocking them from restructuring their debt.
The Vatican did not release an official statement, but Kirchner said she and Francis had talked about an encyclical he wrote last year which criticised the global economic system and which they agreed "seems like it was written for Argentina".
In it the pontiff, who has made fighting for the poor a cornerstone of his 18-month papacy, attacked the "idolatry of money".
He has described "the current economic system, which worships a god called money" as "bringing us to tragedy."
"The pope is very worried for the situation in the world, and shows it continuously," Kirchner said. But she added: "He's not worried about the governability of Argentina."
Kirchner, 61, is struggling to right the economy with just over a year to go in her second and final term.
And with growing discontent in Argentina over the recession, one of Francis's closest associates, Vatican chief of ceremonies Guillermo Karcher, had said ahead of the president's visit that the pontiff was "worried about governability, about a healthy democracy."
Argentina was plunged into economic mire after two American funds bought up defaulted Argentine bonds on the cheap following the country's 2001 economic crisis and then sued the country for full payment in US federal court.
The funds won a decision that derailed Argentina's bid to restructure its debt by barring it from paying creditors who had accepted 70-percent losses without also paying the plaintiffs the full $1.3 billion due.
Kirchner left the Vatican for New York, where she is due to address the UN's General Assembly on Wednesday.
Argentina is lobbying to create a UN convention that would prevent a minority of bondholders from scuppering debt-restructuring plans for countries facing insolvency.
A resolution to negotiate such a framework passed the 193-member General Assembly earlier this month with 124 votes, though the United States and most other major powers voted against or abstained.