Gjorge Ivanov's decision will delay but not derail the deal that Macedonia's parliament has already ratified.
Under the country's constitution, if lawmakers meeting for a second time once again approve legislation that the president has refused to sign off on then the president can no longer block it.
Parliament speaker Talat Xhafer told The Associated Press that lawmakers will probably repeat the vote next week.
In a statement Tuesday, Ivanov's office argued that the agreement is unconstitutional.
The agreed deal with Greece will require several more steps, including a referendum this autumn in Macedonia, before it can be fully implemented.