Sang Kyon-song, president of the International Criminal Court, traveled Monday to Zintan, Libya, to welcome a decision by authorities to release Taylor and her Lebanese, Russian and Spanish counterparts.
Taylor was appointed to help with the legal defense for Saif al-Islam Gadhafi, son of later leader Moammar Gadhafi. Saif al-Islam is wanted by the ICC for war crimes allegedly committed during last year's civil war. Tripoli maintains it has the right to try him in national courts.
Taylor was suspected of passing sensitive documents over to Saif al-Islam from one of his supporters and held since mid-June. The ICC, in a statement, said the circumstances of meetings with Saif al-Islam were "a matter of concern" for Tripoli, which demanded an apology for the incident.
Kyon said the ICC would investigate the matter.
Carr, in a statement, said the decision to release Taylor and her colleagues brought an end to what he described as a "protracted diplomatic" effort.
"I thank the Libyan authorities, in particular Prime Minister (Abdel Rahim) el-Keib and Deputy Foreign Minister (Mohammed Abdel) Aziz, whose personal intervention was instrumental in bringing this matter to a close," he said. "I also acknowledge the goodwill shown by Zintan authorities in coordinating Ms Taylor's release."