The delegation left the Gaza Strip on Friday after holding talks with several Hamas officials.
Russia says Whelan, 50, was caught with a computer flash drive containing classified information.
An Iranian-American doctor has returned to Iran, Iranian state media reported on Monday.
The US official reiterated an appeal for Iran to release American citizens Baquer Namazi, his son Siamak Namazi and conservationist Morad Tahbaz.
Tehran and Washington have denied reports that his release was part of a prisoner swap.
Maher Obeid, member of the Hamas 'political bureau,' said that any prisoner swap must include 'all the symbols, from Marwan Barghouti to Ahmad Sa’adat.'
'It seems that there is now a real possibility for a deal between Hamas and Israel for the release of all the prisoners of war and those missing in action'
A Hamas official was quoted by Hamas-affiliated websites as saying that “there is no qualitative progress in the negotiations conducted with the occupation through mediators.”