Sheikh Khaled al-Khalifa's comments in a newspaper interview clarified his speech to the UN this week calling for a Mid-East body "without exception".
Bahrain has no formal ties with Israel, but the sheikh said it did not matter.
"Let them all sit together in one group... This is the only path to solve our problems," Sheikh Khaled said.
"Why don't we all sit together even if we have differences and even if we don't recognise each other?" he was quoted saying by al-Hayat newspaper.
Correspondents say few Arab governments are likely to accept a permanent regional forum with Israel.
Most Arab states say they will not set up ties with Israel until it signs up to peace deals with the Palestinians and Syria.
Iran, which rejects any prospect of peace with Israel, is even less likely to join a regional block with it. Many Arab governments also view Iran with suspicion.
'Unrealistic'
Asked if the grouping should include regional foes with no relations, Sheikh Khaled was unequivocal: "With Israel, Turkey, Iran and Arab countries."
Bahrain is a strong ally of the United States, which is also Israel's main international backer.
The only Arab countries which have peace treaties with Israel are Egypt and Jordan. A handful of others hold political contacts without normalising relations.
The Arab League has adopted a proposal by Saudi Arabia that relations can only by further normalised if Israel ends its occupation of the Palestinian territories and Syria's Golan Heights.
Sheikh Khaled met Israel's Foreign Minister Tzipi Livni on the margins of the UN General Assembly last year.
He was unperturbed by al-Hayat's suggestion that it was unrealistic to imagine hardline Iranian President Mahmoud Ahmadinejad negotiating with Israel.
"If this is perceived as a dream, well, many dreams have become reality," he said.
Front Page Features