DeMint's office said in a release that McConnell, a Republican from Kentucky, approved the South Carolina Republican's trip after Senate Foreign Relations Committee Chairman John Kerry, D-Mass., tried to block it, The Hill reported.
The Hill said Kerry attempted Thursday to block DeMint's trip as a response to the South Carolina official's hold on two diplomatic nominees from U.S. President Barack Obama's administration.
DeMint and Kerry also disagree over the current political situation in Honduras following the removal of President Manuel Zelaya by the military in June.
Kerry supports a U.S. government-endorsed settlement that would put Zelaya back in power, while DeMint has supported de facto President Roberto Micheletti.
The Hill said DeMint and a congressional delegation were visiting Honduras ahead of the Central American country's Nov. 29 elections.