Final answer:
Portugal and Spain were the two countries that initially sparred over Brazil, with the conflict being resolved by the Treaty of Tordesillas.
Step-by-step explanation:
The two countries that sparred over Brazil in the earliest times of exploration were Portugal and Spain. This conflict over territory was mitigated through the Treaty of Tordesillas, which effectively divided the non-European world into two zones of influence, allotting part of Brazil to the Portuguese sphere of influence. Portugal, under the leadership of figures such as Prince Henry the Navigator, initiated the era of Atlantic exploration and was the first to establish a claim to Brazilian territory when Pedro Cabral reached Brazil.
Later, nations such as France and the Netherlands challenged Spanish and Portuguese control in the Americas, primarily for economic reasons, but the initial sparring for Brazil was between Portugal and Spain.