It was the first time Mr Key had met the Colombian President. He and his wife were welcomed to the El Narino Palace in Bogota by lines of the Presidential Guard along a red carpet.
Relations between the two countries are at a fledgling level and in their meeting the leaders agreed to start work on assessing a potential economic partnership - effectively the first step toward a future free trade agreement.
Mr Key said Colombia was the only one of the four Pacific Alliance countries in Latin America that New Zealand had not agreed a path for open trade and investment. The other countries are Chile, Peru and Mexico.
Mr Santos said he believed Colombia could benefit from New Zealand's expertise in agriculture to develop its farming industry.
Mr Santos also pledged to support New Zealand's bid for the Security Council seat in 2015 while Mr Key said New Zealand supported Colombia's entry into the OECD. Although there is a moratorium on membership of APEC, he said he was certain Colombia would one day be accepted into that forum as well.