He told the Hackney Gazette that the school "believes that women have a choice about whether they want to drive or not, and our policy is to accept all children who are members of our community, which we have been doing for the last 40 years."
He explained that the original letter had been sent on behalf of Belz spiritual leaders who "had not taken into account the implications" of introducing a ban.
Ms Morgan, who is also Minister for Women and Equalities, had ordered an inquiry into the threat to exclude pupils, warning that it could breach independent school rules.
The EHRC also stated that "this sort of discrimination has no place in our society" and it was "unlawful to ban children from school attendance because their mothers, rather than their fathers, drive them there."
British Jewish religious leaders waded into the controversy sparked by last week's JC story. Chief Rabbi Ephraim Mirvis dissociated himself from a view of women "which is both objectionable and at odds with Jewish values".
The Senior Rabbi of the Spanish and Portuguese Jews' Congregation, Joseph Dweck, felt that stopping women driving was "deeply upsetting" and made the Torah seem "restrictive, oppressive and anti-life".
Shadow Equalities Minister Gloria De Piero also wrote to EHRC chairman Baroness O'Neil to call for action.
A leading QC, John Bowers, said that "to require female persons not to drive is an act of sex discrimination" and that schools would be in breach of the Equalities Act if they tried to make it a condition. While he believed that no Belz woman would be likely to sue their schools, a no-drive policy could trigger a formal investigation.
The EHRC said if any pupil were turned away under such circumstances, it could take regulatory steps to prevent recurrence.
While independent schools enjoy a great deal of freedom, they are legally required to "actively promote" British values. These include understanding the importance of combating discrimination; tolerance of those with different beliefs; and respecting other people, particularly with regard to the 2010 Equalities Act.
In a letter last week to Ms Morgan, Mr Klein stated that it had never been Belz's intention to "stigmatise or discriminate against children or their parents for the sole reason that either of the parents drives a car".
Whereas most women in their community did not drive cars, a fair number did so "unhindered", he said. "They and their families are as respected within our community as any other members and we have no intention of changing that."
But he made it clear that the group believed that private schools had the freedom "to set our own high standards."
While a spokesman for Belz had earlier explained that the letter from Mr Klein did not amount to a rejection of the ban, Mr Klein later told the JC that his statement to the Hackney Gazette clarified his position.
Neshei Belz, a women's organ-isation, also issued a statement last week, saying that that driving a vehicle was "a high-pressured activity where our values may be compromised by exposure to selfishness, road rage, bad language and other inappropriate behaviour".
But they added that they did not disrespect those who "conduct lifestyles that are different to ours".
Meanwhile, Hackney Council has asked the main Belz girls school, Beis Malka, to clarify its admissions policy following its application to become state-aided in September.
Beis Malka, which is rated good by inspectors and produces creditable GCSE results, applied to become a free school but was turned down by the government three years ago.
Its application now for voluntary-aided status - which means it would come under the umbrella of the local council - will be considered in late July. Hackney Council said that it would take into account factors such as "equal opportunity and community cohesion".
The Belz schools are also eligible for state subsidy for three- and four-year-olds, but Hackney Council was unable to provide figures.
