The first initiative of its kind in Iraq, a historic foe of Israel and where its sworn enemy Iran has a strong influence, the conference was held Friday.
The organisers, the New York-based Center for Peace Communications (CPC), advocates for normalising relations between Israel and Arab countries, alongside working to establish ties between civil society organisations.
Iraq's Kurdish region maintains cordial contacts with Israel, but the federal government in Baghdad, which has fought in Arab-Israeli wars, does not have diplomatic ties with the Jewish state.
Four Arab nations -- the United Arab Emirates, Bahrain, Morocco and Sudan -- last year agreed to normalise ties with Israel in a US-sponsored process dubbed the Abraham Accords.
"We demand our integration into the Abraham Accords," said Sahar al-Tai, one of the attendees, reading a closing statement in a conference room at a hotel in the Kurdish regional capital Arbil.
"Just as these agreements provide for diplomatic relations between the signatories and Israel, we also want normal relations with Israel," she said.
"No force, local or foreign, has the right to prevent this call," added Tai, head of research at the Iraqi federal government's culture ministry.
However, Iraq's federal government rejected the conference's call for normalisation in a statement on Saturday and dismissed the gathering as an "illegal meeting".
The conference "was not representative of the population's (opinion) and that of residents in Iraqi cities, in whose name these individuals purported to speak," the statement said.
The office of Iraq's President Barham Saleh, himself a Kurd, joined in the condemnation.
Powerful Shiite cleric Moqtada Sadr urged the government to "arrest all the participants", while Ahmed Assadi, an MP with the ex-paramilitary group Hashed al-Shaabi, branded them "traitors in the eyes of the law".
The 300 participants at the conference came from across Iraq, according to CPC founder Joseph Braude, a US citizen of Iraqi Jewish origin.
They included Sunni and Shiite representatives from "six governorates: Baghdad, Mosul, Salaheddin, Al-Anbar, Diyala and Babylon," extending to tribal chiefs and "intellectuals and writers", he told AFP by phone.
Other speakers at the conference included Chemi Peres, the head of an Israeli foundation established by his father, the late president Shimon Peres.
"Normalisation with Israel is now a necessity," said Sheikh Rissan al-Halboussi, an attendee from Anbar province, citing the examples of Morocco and the UAE.
Kurdish Iraqi leaders have repeatedly visited Israel over the decades and local politicians have openly demanded Iraq normalise ties with the Jewish state, which itself backed a 2017 independence referendum in the autonomous region.