If you have time to make contact then the relevant ASTM committee secretary or convenor will know if there is an exact ISO equivalent since they surely would have been a participating member of the ISO working group. It's not my field but this is what I found from the EN and ISO catalogs. There are a few related standards below that I extracted from the lists, but I don't know their degree of equivalence and maybe the organisation issuing the tender won't either, which would be the problem.
CEN textile standards under development (TC248):
http://www.cen.eu/CENORM/Sectors/TechnicalCommitteesWorkshops/CENTechnicalCommittees/WP.asp?param=6229&title=CEN%2FTC+248
CEN textile standards published:
http://www.cen.eu/CENORM/Sectors/TechnicalCommitteesWorkshops/CENTechnicalCommittees/Standards.asp?param=6229&title=CEN%2FTC+248
ISO textile standards under development (TC38):
http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_tc_browse.htm?commid=48148&development=true&includesc=true
ISO textile standards published:
http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_tc_browse.htm?commid=48148&published=true&includesc=true
EN ISO 5470-2:2003 Rubber- or plastics-coated fabrics - Determination of abrasion resistance - Part 2: Martindale abrader (ISO 5470-2:2003)
EN ISO 5981:2007 Rubber- or plastics-coated fabrics - Determination of resistance to combined shear flexing and rubbing (ISO 5981:2007)
EN 14119:2003 Testing of textiles - Evaluation of the action of microfungi
EN ISO 13935-1:1999 Textiles - Seam tensile properties of fabrics and made-up textile articles - Part 1: Determination of maximum force to seam rupture using the strip method (ISO 13935-1:1999)
EN ISO 13935-2:1999 Textiles - Seam tensile properties of fabrics and made-up textile articles - Part 2: Determination of maximum force to seam rupture using the grab method (ISO 13935-2:1999)
EN ISO 13936-1:2004 Textiles - Determination of the slippage resistance of yarns at a seam in woven fabrics - Part 1: Fixed seam opening method (ISO 13936-1:2004
EN ISO 13936-2:2004 Textiles - Determination of the slippage resistance of yarns at a seam in woven fabrics - Part 2: Fixed load method (ISO 13936-2:2004)
EN ISO 13936-3:2007 Textiles - Determination of the slippage resistance of yarns at a seam in woven fabrics - Part 3: Needle clamp method (ISO 13936-3:2005)
EN ISO 3759:1995/AC:1999 Textiles - Preparation, marking and measuring of fabric specimens and garments in tests for determination of dimensional change (ISO 3759:1994)
EN ISO 5077:2008 Textiles - Determination of dimensional change in washing and drying (ISO 5077:2007)