It is not every day that diaspora Jews are encouraged by Israelis to intervene in their country's affairs. But a few weeks ago an advertisement in this newspaper urged readers to petition the Israeli government.

You would not call its instigators left-wing; the advert was placed by Tzohar, an association of modern Orthodox rabbis. What led them to do this was the latest instalment of a controversy as old the state itself, the question of who is a Jew.

Israel's government is now pushing through a reform of conversion procedures, which is backed by Tzohar but opposed by the Israeli Chief Rabbinate and the Charedi leadership. The new measure would extend the power to perform conversions to town rabbis rather than confine it to rabbinic courts under the Chief Rabbis' direct control.

At stake is much more than rabbinic prestige or bureaucracy. Tzohar and others believe that it may eventually help a large number of Israelis who are trapped in a kind of Jewish limbo.

Under the Law of Return, the cornerstone of Zionism, the children of a Jewish father but non-Jewish mother can come to live in Israel and automatically claim citizenship. They can speak Hebrew, have Israeli friends, serve in the army - but the Orthodox authorities will still not accept them as Jewish. They will not legally be able to marry another Jew in Israel unless they convert because Israel has no civil marriage. If they die in defence of their country, they may be denied burial alongside comrades in an Orthodox cemetery.

A more flexible orthodox conversion policy could help avert social schism

More than a quarter of a million of Israelis who came from the former Soviet Union in the great exodus in the 1990s are thought to be in this predicament. Tzohar suggests that as many as 700,000 "Jewish-born" Israelis are now prevented from having a chupah in Israel because the rabbinate does not recognise them.

Supporters of the conversion change believe that town rabbis might adopt a more lenient approach towards converts rather than insist on standards too exacting for most. It is not that converts would simply be nodded through: but they might pass muster if they could broadly show a commitment to Jewish peoplehood and tradition rather than be expected to adopt a strictly Orthodox lifestyle down to the last mitzvah.

A more flexible Orthodox conversion policy could help integrate many Israelis into Israeli Jewish society and avert a looming social schism, according to its proponents. The Chief Rabbis will have none of this. They threaten not to recognise conversions conducted outside their aegis and Ashkenazi Chief Rabbi David Lau now wants an overhaul of the Law of Return, which would apply it only to those born of a Jewish mother.

But some rabbis argue that there is compelling case in Jewish law for treating conversion candidates with a Jewish father sympathetically. Four years ago an independent-minded Israeli Sephardi rabbi, Haim Amsalem, published a book, entitled Zera Israel, which showed why Orthodox rabbis should be opening the door a little wider to patrilineal Jews.

Zera Israel means "Seed of Israel". The phrase crops up in the Bible - it is used by Isaiah and Nehemiah - and has long been interpreted to refer to descendants of Jews who may not be considered Jewish under Jewish law. For some rabbis, it is more than just desirable to reclaim patrilineal Jews; there is a duty to stretch out a helping hand. Israel's first Sephardi Chief Rabbi, Ben-Zion Meir Hai Uziel, who was known for his leniency on this issue, quoted the divine rebuke in the book of Ezekiel for the failure to gather in lost sheep, "You have not brought back those who have strayed, nor have you sought those who were lost".

Not only in Israel, of course, does the protracted wrangle over Jewish status leave faultlines under the Jewish people. Among the mostly dwindling diaspora populations is an unknown number of Zera Israel.

Those who call for a less rigid Orthodox conversion policy tend to justify this largely in the context of Israel, where someone is more likely to be absorbed into Jewish society, speaking a Jewish language and living by a Jewish calendar. But there is no reason not to invoke the idea of Zera Israel in the diaspora, too.

Opting out of Jewish life is easy enough, whatever your Jewish parentage. So for those Jews of patrilineal descent who want to opt in and are actively involved in the Jewish community, there must be some way to regularise their status so that they are universally accepted as Jewish, without demanding that they become nouveau Charedim.

An American Orthodox rabbi, J.Simcha Cohen, in his 1987 book, Intermarriage and Conversion, argued that Jewish law actually permits a Beth Din to convert the child of a Jewish father even without the condition of observing "the yoke of the commandments". Orthodox authorities, here as elsewhere, have been reluctant to use such discretion, fearing that it would amount to a licence to intermarriage.

But is worth recalling that each day in the morning service, the paragraph after the Shema holds out the promise of God's word enduring forever, "for our children and all our generations and for all future generations of Zera Israel, the Seed of Israel". Restoring lost Jews is a spiritual imperative as much as a national mission.