You can't enter an international phone number in the Mailing Address & Phone number section of the Personal Interview (or in any of your TurboTax account records).
The IRS asks for your phone number in case they have a question about your return (this is rare). They cannot, however, call an international phone number. TurboTax representatives cannot call international numbers, either.
In order to complete and e-file your return, you can enter the phone number of a relative or friend in the U.S,, or a "dummy number" (800-555-1212). The IRS will identify your entry as a placeholder number - if they have questions, they will mail them to you.
Remove all dashes and use only your phone number - no country code. If you have an issue when trying to e-file with a non US phone number, see the message below.
There seems to be an issue with e-filing when there is not a US phone number listed in your Intuit Online account. When you are signed into your account, click on Intuit Account in the bottom left corner. The error is not from the phone number on your tax return but rather the phone number attached to your Intuit (TurboTax) account.
Change your phone number to a US number in the Intuit Account of Turbo Tax. No need to verify this number in the Intuit Account just click exit when you are done. Then go back to your return and continue filing. Don't use a Google Voice number, a Skype number, or any other non-US or non-verifiable phone number. Again, you don't have to verify the number but the number needs to be verifiable.
You may be able to leave the phone number field blank on your Intuit account and e-file your return. No matter which option you use, make sure to update your account with your correct phone number once your return is e-filed.