A fresh round of talks between the DUP and Sinn Fein on the issue took place on Monday night, and more discussions are taking place on Tuesday.
Sammy Wilson, the DUP Finance Minister, said the Monday night talks had been "productive" and "friendly."
However, he said the idea of a deal within days was unrealistic.
Northern Ireland Secretary Shaun Woodward and the Irish Minister for Foreign Affairs Micheal Martin are also to meet, as the governments step up pressure on the parties to resolve the issue.
Temporary
Mr Robinson announced on Monday he was stepping aside for six weeks, and Mrs Foster has insisted her role is temporary.
"After six weeks either Peter comes back or there is a new election to the Office of First Minister and Deputy First Minister," she said.
Mrs Foster said that anyone in the party who was supporting the leader in public but saying they believed his position was untenable in off-the-record conversations to the press should "have the courage of their convictions and come out".
"He is not stepping down, he is just stepping aside for a short period of time to deal with very understandable issues in relation to his wife and, indeed, the one political allegation that has been made against him," she said.
The Northern Ireland Assembly is to investigate the Robinsons' conduct
On Monday night, the BBC's Panorama reported that not all of the money received by Iris Robinson's young lover, Kirk McCambley, has been paid back to a property developer, Ken Campbell.
Mr Campbell's solicitor said the money had been an interest-free loan of £25,000 and that £5,000 had still to be repaid, adding, "our client expects to be fully repaid and Mr McCambley's debt cleared."
Mrs Robinson, the MP for Strangford, had obtained the £25,000 from Mr Campbell and a further £25,000 from another developer, the late Fred Fraser.
She failed to register the transactions with the Westminster or Stormont authorities.
The Northern Ireland Assembly's Committee on Standards and Privileges is to investigate the conduct of both Robinsons to see if any breaches of the assembly's code had occurred.
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