The official said the talks "will probably continue on Wednesday" following a meeting between the Greek government and senior bank negotiators.
"There are some details to be worked out," the official added.
Greek Prime Minister Lucas Papademos and Finance Minister Evangelos Venizelos had earlier met with Charles Dallara, managing director of the Institute of International Finance and Jean Lemierre, a senior advisor to France's BNP Paribas.
The IIF represents over 450 financial institutions worldwide.
The so-called private sector initiative has been expected to result in banks taking at least a 50 percent "haircut" on their Greek debt, which would remove about 100 billion euros ($127 billion) from the country's massive debt of 350 billion euros.
Greek media on Friday reported that a disagreement has surfaced on the interest rate of new government bonds that will be issued to credit holders in return for maturing debt being phased out under the planned deal.
The Kathimerini newspaper said private sector negotiators want new debt obligations to be repaid at about a five percent interest rate, whereas Greek officials are only willing to agree to a level of around four percent.
After initial meetings Thursday, the IIF put pressure on Greece, saying "time for reaching an agreement is running short."