ATHENS (Reuters) - The chief negotiator for private creditors over a Greek debt swap deal, Charles Dallara, urged lawmakers to approve the country's IMF/EU bailout deal in parliament on Sunday, saying the deadlines allowed "no room for slippage."

In a newspaper interview published on Saturday, Dallara, who is managing director of the International Institute of Finance (IIF), said private creditors were committed to a voluntary agreement and that he was convinced the scheme would be a success.

"I want to encourage them to vote for it ... it is important for lawmakers to understand what is at stake," Dallara told Kathimerini newspaper.

"I am convinced that the (debt swap) agreement will find support in the markets, in the shape it is taking and with the EU's significant support," he said. "We expect a very high voluntary participation rate."

Dallara, however, said deadlines to complete the debt swap were tight, and there was "no room for slippage."

The Greek parliament votes on Sunday on the 130 billion euro rescue package, which includes a further 3.3 billion euros in deeply unpopular budget cuts this year. Greece needs the funds by next month to avoid bankruptcy.

Finance Minister Evangelos Venizelos said on Saturday the country had until February 17 to submit the debt swap offer to private sector bondholders, before a March 20 deadline to repay bonds worth 14.5 billion euros.

Asked whether the European Central Bank should also accept value reductions on their bond holdings, Dallara told the newspaper: "It is important that everyone shares a fair part of the burden."

(Reporting by Harry Papachristou; Editing by David Stamp)