Organizers declined to say whether the meeting, attended by some 30 participants helped bring the two sides closer.
Meeri-Maria Jaarva, a spokeswoman for the conflict-prevention group Crisis Management Initiative, confirmed the meeting was over, but declined to comment further.
The group, headed by former Finnish President Martti Ahtisaari, convened the seminar together with the John W. McCormack Graduate School of Policy Studies of the University of Massachusetts Boston.
Finnish broadcaster YLE said several of the participants left the meeting on Sunday, while the rest were expected to leave on Monday or Tuesday.
Ahtisaari, who did not attend the meetings, said it was now up to the Iraqis whether they want to continue the process started in Finland, YLE reported.
Although organizers have declined to identify participants, representatives of the radical Shiite cleric Muqtada al-Sadr, the leader of the largest Sunni Arab political group, Adnan al-Dulaimi, and Humam Hammoudi, the Shiite chairman of the Iraqi Parliament's foreign affairs committee, are reported to have attended the seminar.
Officials from South Africa and Northern Ireland also attended.
The venue and other details were kept secret to allow the participants to meet in peace, Jaarva said.
Ahtisaari and his group have facilitated peace talks for other conflicts. In 2005, Ahtisaari helped end 30 years of fighting between Aceh rebels and the Indonesian government with peace talks in Finland, which he initiated and mediated with CMI.