Final answer:
Thomas Jefferson resolved the threats from the Barbary Pirates by combining military force, including naval engagements and blockades, with diplomacy, resulting in the First Barbary War and a subsequent settlement that ceased the payment of tributes, establishing U.S. naval presence and commitment to protecting its commerce.
Step-by-step explanation:
President Thomas Jefferson solved the Barbary Pirates problem through both a show of military force and careful diplomacy. Faced with threats to American shipping by the pirates from the North African Barbary States, who demanded tribute to allow safe passage, Jefferson initially tried diplomacy but eventually deployed the U.S. Navy to the Mediterranean. This led to the First Barbary War (1801-1805). Instead of continuing to pay tributes, which was the standard European practice, Jefferson's administration engaged in naval battles and blockades against Tripoli, one of the Barbary States. The conflict ended with a negotiated settlement that included a ransom for American prisoners but no future tribute.
The use of military force marked a significant change in U.S. foreign policy, as Jefferson had previously aimed to reduce military expenses and avoid entanglement in foreign wars, as evidenced by his reduction of the army and navy. However, the issue with the Barbary Pirates was seen as a direct attack on American sovereignty and commerce, requiring a decisive response. The success of Jefferson's approach established the principle of free navigation of the seas and signaled to foreign powers that the United States was willing to defend its interests militarily, if necessary.