Which of these asserted that the united states had the right to intervene in the affairs of neighboring american countries, to counter threats posed to its security and interests?

Monroe Doctrine and Roosevelt Corollary--the Monroe Doctrine first set the policy that the western hemisphere was closed to colonization. The Roosevelt Corollary took it a step further by providing military behind the policy. 

Following the independence movement in the US and throughout Latin America, the US wanted to protect the area from future colonization. The Monroe Doctrine made the statement and then 80 years later the Roosevelt Corollary enforced the doctrine with our navy and army force.