By Nektaria Stamouli and Viktoria Dendrinou 

ATHENS--Prime Minister Alexis Tsipras said Friday a report by the International Monetary Fund laying out Greece's worsening economic situation vindicates his country's demand for debt relief and its choice to reject its creditors' bailout proposals so far.

In his third televised address to his nation in the past week, Mr. Tsipras called again on Greeks to vote "no" in a referendum on Sunday on creditors' demands. Opinion polls suggest the referendum is too close to call, with "yes" and "no" running neck-and-neck but momentum possibly swinging away from the government.

Earlier this week, polls showed a lead for the "no" camp. But the continued closure of Greece's banks, first ordered on Monday, seems to have swayed public opinion, with many Greeks worrying such a vote could deepen the country's financial paralysis and deal a devastating blow to its already depressed economy.

The IMF warned in a detailed review of Greece's debt the day before that the country would need "comprehensive" debt relief and more than EUR60 billion ($66.6 billion) in new aid to return to financial health.

Mr. Tsipras has sought to reassure Greeks they don't have to fear the consequences of voting against creditors' demands for painful economic overhauls, which his government rejected last week in talks with the eurozone and IMF in Brussels.

"The IMF report justifies our choice not to accept a deal that bypasses the major issue of debt," Mr. Tsipras said in a televised address. European governments that supplied the bulk of Greece's bailout program, which expired on Tuesday, have so far refused to offer Greece significant debt relief.

The "yes" and "no" camps were planning separate rallies for Friday evening.

Greece's Council of State, the country's highest administrative court, ruled that Sunday's referendum procedure is legal and could go ahead as planned, a court official said.

The court decided on the legality of the referendum after two citizens argued that it breaches Greece's constitution.

A survey by polling institute Alco published Friday by the ProtoThema website found 41.7% of respondents planned to vote "yes" in Sunday's referendum, while 41.1% planned to vote "no." The survey questioned 1,400 people between Wednesday and Friday.

The finding is well within the margin of error, which Alco put at 3.1 percentage points, indicating that Greeks are roughly equally split on Sunday's question.

Another poll published Friday and commissioned by Bloomberg News also showed a virtual tie, with 43% of responders planning to vote "no" while 42.5% backed "yes." The survey, conducted by the University of Macedonia Research Institute of Applied Social and Economic Studies, asked of 1,042 people and had a 3-percentage-point margin of error.

A third survey on Friday by Public Issue for the Avgi newspaper, affiliated with the ruling leftwing Syriza party, found that 42.5% of the 1,053 respondents said they would vote "yes" and 43% backed "no."

Mr. Tsipras reiterated his claim that a "no" victory in the referendum would mean a "continuation of the negotiations" with creditors, and a deal "with better terms."

That assertion clashes with warnings from Europe, where policy makers have said a "no" vote would severely harm the chances for a deal with Greece and could increase the prospect of its exit from the eurozone and financial collapse.

Officials from Germany and other creditors have said any new bailout program would require tougher measures than those Greeks are now being called upon to reject, because Greece's closed banks and capital controls are degrading its economic outlook.

"If we want to negotiate a third program, it will be much tougher than the second program, inevitably... that's independent of whether we are getting a 'no' or 'yes' on Sunday evening," said Belgian Finance Minister Johan Van Overtveldt.

In Athens, Berlin is widely seen as the main driver of Greece's creditors' tough line. German Finance Minister Wolfgang Schäuble, whose stern face appears in Greece on posters for the '"no" campaign, told the German newspaper Bild that he would expect difficult negotiations because Greece's situation has "worsened dramatically."

Mr. Schäuble stressed that any negotiations would take place "on a completely new basis and under more difficult economic circumstances."

Mr. Schäuble will in the coming weeks claim back EUR532 million from aid earmarked for Greece's second bailout package, a German finance ministry spokesman said Friday. The funds have been unclaimed since the program ended Tuesday night.

Those funds represented the profits Berlin made last year on the holdings of Greek bonds at the German central bank, which Berlin had pledged to provide to Greece.

Berlin had also been due to transfer EUR412 million in earned interest for 2015 on July 1 to Greece, but it stopped the transfer after the Greek government walked out of the bailout talks last weekend.

Meanwhile, easing some of the pressure on Greece, eurozone governments decided Friday not to ask Greece for an immediate repayment of rescue loans from the currency union's bailout fund.

The European Financial Stability Facility has lent Greece EUR144.6 billion in recent years and the terms of those loans allow the fund to seek immediate repayment if a borrower defaults on the IMF. Greece missed a EUR1.56 billion payment to the IMF on Tuesday.

Viktoria Dendrinou in Athens and Andrea Thomas in Berlin contributed to this article

Write to Nektaria Stamouli at nektaria.stamouli@wsj.com and Stelios Bouras at stelios.bouras@wsj.com