Alvaro Uribe, the Colombian president, issued a statement earlier saying he was ready to re-establish diplomatic relations with Ecuador immediately.
A statement from the Atlanta-based Carter Centre said the former US president had consulted with both sides recently "about the possibility of renewing diplomatic relations between the two countries immediately and without preconditions, initially at the level of charge d'affaires".
Carter worked with the UN Development Programme to support a dialogue group composed of citizens from both countries to improve relations, the statement said.
Colombian troops raided a Farc camp in the Ecuadorean jungle on March 1, killing about 20 people, including Raul Reyes, a Farc leader, as well as four Mexicans and an Ecuadoran.
Both Correa and Hugo Chavez, the Venezuelan president, broke diplomatic ties with Colombia over the raid and ordered soldiers to their borders.
Despite the re-establishment of diplomatic ties, tensions remain between the two neighbours.