Tensions flared over the issue as Mr Chavez warned on Saturday that if Mr Palmer arrives in Venezuela he would be detained and put on the next flight home. Mr Palmer angered Mr Chavez by suggesting during the Senate confirmation process that morale is low in Venezuela's military and that he is concerned Colombian rebels are finding refuge in Venezuela.
Mr Chavez, for his part, has publicly been saying for months that Mr Palmer would not be welcome under any circumstances.
"They've made this decision, and obviously we will evaluate what to do," Mr Crowley told reporters. "We will evaluate the consequences to our relationship."
He would not comment on possible U.S. responses.
A Venezuelan foreign ministry official, Temir Porras, presented a formal diplomatic protest on the matter to the U.S. Embassy's charge d'affaires, Darnall Steuart, during a meeting Monday in Caracas. Mr Steuart said the U.S. regrets Venezuela's stance, and it "will bear the responsibility for that action."
Mr Chavez said Mr Palmer had "disqualified himself" with his remarks. Addressing his foreign minister on Saturday, Mr Chavez that if Mr Palmer were to arrive at Caracas' airport, he should be stopped.
"Give Mr. Palmer a coffee from me, and then 'bye-bye.' He cannot, he cannot enter this country," he said.