Zelaya was flown to Costa Rica after being taken into military custody at his house outside the Honduran capital.
Zelaya told a local television station Sunday that he is at the airport in San Jose, capital of Costa Rica. He said he would not recognize any attempt to name a replacement for him following his detention earlier Sunday.
Zelaya says he will be meeting with diplomats and stressed he wanted to serve out his term, which ends in early 2010. He called for talks.
Zelaya was detained by army troops early Sunday, shortly before he was to have held a controversial referendum on constitutional reform opposed by most of the rest of the Honduran government.
Secretary of State Hillary Rodham Clinton says the action taken against Honduras' president should be condemned by everyone. She says Honduras must embrace the principles of democracy and respect constitutional order.