<Page> EXHIBIT 23.1 INDEPENDENT AUDITORS' CONSENT We consent to the incorporation by reference in Registration Statement Nos. 333-30642, 333-56998, 333-67780, and 333-73492 on Form S-8, Registration Statement No. 333-53756 on Form S-3 of iBasis, Inc. of our report dated February 27, 2004, (which report expresses an unqualified opinion and includes an explanatory paragraph relating to a change in the method of accounting for goodwill and other intangible assets), appearing in the Annual Report on Form 10-K of iBasis, Inc. for the year ended December 31, 2003. /s/ Deloitte & Touche LLP Boston, Massachusetts February 27, 2004