Barak's comments come a day after a Jewish American businessman revealed that he had given Olmert large amounts of money, some of which had been in personal loans.
Morris Talansky told the Jerusalem District Court on Tuesday that he had loaned Olmert hundreds of thousands of dollars to cover the Israeli leader's political activities over a 15-year period.
In his testimony, Talansky said he had been asked to pick up a $4,700 bill from a three-day stay by Olmert at a New York hotel.
Talansky also said that he loaned Olmert as much as $30,000 for a holiday in Italy.
Olmert, who has denied any wrongdoing, has acknowledged receiving money from Talansky but said the funds were legal election campaign contributions.
Olmert's defence attorneys will cross-examine Talansky only in July.
Coalition in danger
Reporting on the latest developments, Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said: "There have been no threats, no ultimatums - basically he [Barak] is calling on Mr Olmert himself to take responsibility - to put Israel's interests above his own.
"People have been really quite disgusted and shocked by the allegations [against Olmert] ... I think Ehud Barak is striking a note with Israeli public opinion when he says 'enough is enough'."
If Olmert were to step aside temporarily while prosecutors pursue the investigation into allegations of bribery against him, Tzipi Livni, the foreign minister, would be likely take over for an interim period of 100 days.
In his news conference, Barak put the onus on Olmert's Kadima party to seek a new leader to replace the prime minister, but said his Labour party could force an early election if Olmert refused to go.
Barak's party is Olmert's main coalition partner in the Israeli parliament and its withdrawal from the government would almost certainly force an early election.
But polls indicate that the opposition Likud party, led by Benjamin Netanyahu, could be the strongest party after any snap election.
The political turmoil threatens to derail US-efforts to secure an Israeli-Palestinian peace deal before George Bush, the US president, steps down in January.
|The corruption allegations appear to have |
damaged Olmert's standing with Israelis [AFP]
Nour Odeh, Al Jazeera's correspondent in Ramallah, said Mahmoud Abbas, the Palestinian president, was concerned about the peace process should Olmert step down.
"The office of the Palestinian prime minister said this crisis could derail the peace process, not necessarily because the peace process is going so well ... but because of opinion polls in Israel that suggest if any elections are held in Israel at the moment Benjamin Netanyhau, the right-wing Likud leader, could be prime minister," she said.
"That certainly would not be good news for anyone involved in a peace process with Israel, as far as the Palestinians are concerned - they have tried with Netanyahu before and they would not particularly look forward to dealing with him again."
Marwan Bishara, Al Jazeera's senior political analyst, said some reports had emerged of suspicions about "why suddenly a witness came all the way from New York to talk about cash being handed to Mr Olmert".
"Is it coincidental that just when Mr Olmert is speaking about the possibility of peace with Syria new corruption charges are creeping against him?" he said.
"There are some suspicions out there - in Israel and outside Israel - that maybe just because there is some talk of peace and perhaps reaching a deal with the Palestinians this year that certain segments of the Israeli security establishment are interested in sidelining Mr Olmert."