The basic reason for which the United States supported the Panamanian rebels was the US's desire to build a canal across the Isthmus of Panama. The US had been negotiating with Colombia for the right to build this canal. However, the Colombian Senate overwhelmingly rejected the treaty that would have given the US this right.
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They wanted the colonists to stay under their rule. When they went off to form a new nation, this was scary for them because now they had an opposing threat.
