Rehn welcomed "progress" made toward meeting EU-IMF demands that Cyprus reform its financial sector and raise 5.8 billion euros to unlock 10 billion euros ($13 billion) in desperately needed emergency loans by a Monday deadline.
Cypriot leaders face a make-or-break meeting of eurozone finance ministers on Sunday evening, their last chance to get a deal.
"It is essential that an agreement is reached by the eurogroup on Sunday night," said Rehn, who is the EU economy and euro commissioner.
He acknowledged that Cypriot leaders faced hard choices to try to limit the damage to the economy from the blow to its bloated banking sector, after a firestorm of protest over EU plans to impose a special levy on bank accounts.
But he added: "Unfortunately, the events of recent days have led to a situation where there are no longer any optimal solutions available. There are only hard choices left."
German Finance Minister Wolfgang Schaeuble also warned Cyprus that if it was to stay in the eurozone it had to meet the terms of the rescue package.
"The eurozone countries want to help Cyprus, but the rules must be respected, the aid must be relevant and the programme must tackle the problems at their root," he said in comments published Sunday in Germany's Welt am Sonntag.
Talks went on until nearly midnight (2200 GMT) Saturday to try to find a way to meet the EU-IMF conditions.
Media reports suggested Cypriot officials had made progress with EU and IMF representatives, having agreed a 20 percent haircut on Bank of Cyprus and a 4.0 percent levy on other banks hours ahead of the Brussels talks.
Privately run Mega TV said the government had reached agreement on most elements of a deal, but the final stumbling block might not be settled before the crunch 1700 GMT talks between President Nicos Anastasiades and EU ministers.
The Cypriot parliament has already approved a painful package of banking reforms and there was reluctant consensus on a raft of other revenue-raising measures to put to the eurozone ministers.
A radical restructuring of the island's second largest lender Laiki (Popular Bank) will see all deposits over 100,000 euros put into a "bad bank" where they will be tied up for years and may never be recovered in full. MPs passed that measure on Friday night.
But negotiations stumbled on EU-IMF demands for a substantial levy on deposits above the same threshold in Bank of Cyprus to avoid it being subjected to a similar restructuring. The bank is the island's largest lender, with more than a third of all deposits.
On Tuesday, MPs flatly rejected an earlier plan for a levy on all bank deposits.
The Cypriot president has invited all the island's party leaders to accompany him to Brussels in a bid to persuade eurozone ministers that there will be no repetition of that defeat.
Mega TV said the remaining sticking point was over whether Bank of Cyprus should absorb the "good bank" carved out of Laiki, or whether they should remain two separate lenders as the government wants.
Cyprus negotiators had been desperate to avoid Bank of Cyprus being subjected to the same bitter pill imposed on Laiki.
A threat to Bank of Cyprus's pension fund sparked an angry march by bank staff on parliament on Saturday and a threat of industrial action.
"If you don't secure our pension fund, we will go on strike from Tuesday," when branches are finally scheduled to reopen after a closure of more than a week, banking union chief Loizos Hadjicostis said.
The strike threat was a serious one for an economy reeling from the prolonged bank closure, imposed for fear of a run by panicked depositors, which has seen many businesses accept only cash transactions.
The streets of Nicosia were otherwise largely deserted Saturday, as anxious residents waited to see how the crisis plays out.
"People don't know if they will have money tomorrow or the day after," said Yiorgos Andoniou, a jobless 57-year-old.
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