The voting is likely to be shifted to September and the current Swedish presidency of the 27-European bloc hopes that the matter will be settled then.
"We've spoken to several party group leaders and no decision is going to be made on Mr. Barroso in July in the European Parliament," Swedish Prime Minister Fredrik Reinfeldt was quoted by the Reuters news agency as saying at a news conference in Stockholm last Thursday.
National governments expressed political support to Barroso at a summit in June and wanted the holding of the voting in July.
However, some political groups in the European Parliament, including the Socialists, the Liberals, the Greens and the extreme Left, objected to the vote in July explaining that swift procedure was legally and technically groundless.
If parliament backs him for another term, Mr Barroso will be charged with putting together a new commission.
Barroso, a former Portuguese Prime Minister, succeeded Italian Romano Prodi in the office of the President of the European Commission in November 2004.