Presidential advisor Ali Rabiei told Sunday's Hamshahri daily that the step was justified on the grounds of the law's effects on society.
The Supreme National Security Council is the top body in the Islamic Republic for deciding on security issues, and Pezeshkian is hoping that it will moderate the new hijab law, at least to some extent.
The law passed by hardliners in parliament provides for large fines and the denial of state services to women failing to heed the obligation to cover their heads.
Prominent people are to be punished particularly severely, with bans on exercising their professions and on travelling abroad, along with the confiscation of up to 5 per cent of their assets.
Sharp criticism of the law, from within the government as well, led to a delay in its enforcement.
Pezeshkian is reported to be against it for fear of resistance in Iranian society and renewed popular unrest.
Observers consider the legislation part of a power struggle between hardliners and moderate forces, and thus a challenge to Pezeshkian.
If he is unable to succeed against the hardliners, the moderate course he pledged during his campaign is believed to be in jeopardy.
Many Iranian women in the larger towns and cities are now refusing to heed the strict dress code imposed by the Islamic authorities.
The trend emerged from the "Woman, Life, Freedom" movement that arose during the autumn 2022 protests.
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