* Fernandez says will only act under international law
* Analysts say tensions could escalate if oil found (Updates with Fernandez and analyst quotes)
PLAYA DEL CARMEN, Feb 22 (Reuters) - Argentine President Cristina Fernandez said Latin American leaders backed her objections to oil exploration in the British-controlled Falkland Islands as drilling of the first well began on Monday.
Argentina, which has claimed the South Atlantic islands known as the Malvinas in Spanish since Britain established rule in the 19th century, invaded them in 1982. After a two-month war, it was forced to withdraw, but still claims the archipelago and says oil exploration by Britain's Desire Petroleum DES.L is a breach of sovereignty.
"There continues to be systematic violation of international law that should be respected by all countries," Fernandez told the opening session of a regional summit near the Mexican resort town of Playa del Carmen.
"In the name of our government and in the name of my people I am grateful ... for the support this meeting has given to our demands," Fernandez said.
Mexican President Felipe Calderon said in the closed-door meetings the group had approved a document supporting Argentina in the territorial dispute, Argentine diplomatic sources said.
Venezuelan Hugo Chavez addressed Britain's Queen Elizabeth directly on his weekly television program, telling her to return the Falklands to Argentina. He repeated his demand late on Sunday when he arrived in Mexico for the summit.
"We support unconditionally the Argentine government and the Argentine people in their complaints," Chavez told reporters at the airport. "That sea and that land belongs to Argentina and to Latin America."
Escalating the dispute, Argentina formally objected to British-led drilling plans near the islands, and said it would require all ships from the Falklands to obtain permits to dock in Argentina.
Fernandez said Argentina would not consider more serious measures like shipping blockades.
"Argentina will not take any step that is not framed in international law," she told reporters.
While the Falklands are not an oil producer and have no proven reserves, oil companies are betting offshore fields may hold billions of recoverable barrels of oil.
Desire Petroleum said it broke ground at a well on its offshore "Liz" prospect, which could contain up to 400 million barrels, although there is a possibility the exploration will recover nothing.
Some analysts doubt the diplomatic bluster will have much effect until the size of the oil deposit is determined.
"Noise will probably continue, but tensions will probably subdue in the next few weeks. However, if results are in fact positive, tensions between the two countries could rise substantially," Eurasia Group's Daniel Kerner wrote in a research note. (Additional reporting by Guido Nejamkis in Buenos Aires; Writing by Mica Rosenberg; Editing by Eric Walsh)