Form 1023 is to become a charitable 401(c)(3) organization.
To become another type of tax-exempt organizations it would be Form 1024 or 1024-A. However, those donations to those types of organizations may not be tax-deductible by the donor. There is a difference between "charitable (which donations may be deductible) and "tax-exempt".
But as Opus said, in MOST cases being a qualified charitable 401(c)(3) organization will NOT allow the US donors to deduct the contributions if the organization is not US based.
I HIGHLY recommend finding a US tax professional that is experienced with tax-exempt organization for assistance. Also there is much more than just filing the initial application (there is required accounting and an annual tax return).
