The Arcadia and Adonia were both scheduled to visit Argentina next month following calls in the Falkland Islands, The Sun reported. Argentina claims the islands, which it calls the Malvinas, and has recently stepped up demands Britain negotiate a change of sovereignty.
Both ships had been scheduled to visit Argentina during round-the-world cruises.
"We're unable to gain assurances that our ships will be allowed to call into Argentine ports," a P&O spokesman said.
Hattie Kilmartin, a restaurant owner in the Falklands, said Argentina is using "bullying tactics" in an effort to destroy the economy.
A referendum has been scheduled for March. Most of the current population of the Falklands is of British descent, and voters are expected to choose to keep the status quo.