The activist fund has built a stake of 9 percent in TIM to try to shake up the way Vivendi has been running Italy's biggest phone group.
Elliott and the French investor were meant to face off for the first time at the Tuesday shareholder meeting.
TIM will still hold its AGM on Tuesday to approve financial results and confirm Amos Genish as chief executive, but the standoff over the board seats will now be delayed to another shareholder meeting scheduled for May.
Paul Singer's fund had called for six Vivendi-nominated board members, including TIM Chairman and Vivendi CEO Arnaud de Puyfontaine, to be replaced with well-known Italian business leaders to help improve governance and strategy.
But following Elliott's move, eight board members nominated by Vivendi resigned, triggering a vote on a full board renewal at a separate shareholder meeting called for May 4.
Despite the mass resignations, TIM's statutory auditors included Elliott's proposal on the agenda for this week's meeting - a decision TIM's board and Vivendi had challenged in court and which the judge suspended with its ruling.
Explaining the decision, the judge said the mass board resignations made it necessary for shareholders to elect an entire new board rather than vote on partial changes that would be temporary.
TIM had no immediate comment, Vivendi declined to comment, while Elliott could not immediately be reached for a comment.
TIM shares were up 0.3 percent by 1020 GMT compared with a flat Milan blue-chip index.