The chances of a digital tax on large internet companies like Facebook and Alphabet Inc.’s Google vanished Nov. 28 when Ireland, Sweden, Denmark and Finland refused to agree to impose the temporary 3 percent levy.

At a preliminary meeting of ambassadors, who gathered to prepare agenda details for the bloc’s Dec. 4 meeting of finance ministers, the Nordic nations and Ireland were joined by Germany, the U.K., and the Netherlands in opposition, according to officials that attended the meeting.

The...