Yes, you can say Navkar (Namokar) Mantra during periods.

In Jain Dharma:

• Menstruation is a natural body process, it does not make the soul impure.
• There is no restriction on:

- Reciting Navkar Mantra (mentally or softly) - Doing jap, prarthna, dhyan at home

• What is usually avoided during periods:

- Going into the garbhagriha (inner temple sanctum) - Touching murtis, pooja items, or scriptures - Doing abhishek, aarti, dravya-puja

Both Shwetambar and Digambar traditions allow Navkar Mantra japa during periods as bhav-bhakti (inner devotion). Only some outer temple rules are paused for a few days, not your prayer.

You can read a simple, related explanation here: “Can I write Navkar Mantra during periods?”