JESUS CARRANZA, Mexico, Nov 16 (Reuters) - More than 1,500 members of a migrant caravan that set off toward the U.S. border from southern Mexico last month have been issued documents to regularize their stay in Mexico, the migration authority said on Tuesday. The National Migration Institute (INM) said it had given 1,574 foreign nationals migration cards and ensured they could work in Mexico since the caravan set off on Oct. 23. Enduring adverse weather and under pressure from officials to give up, the caravan containing many women and children has made slow progress through southern Mexico, and on Tuesday moved into the Gulf state of Veracruz from neighboring Oaxaca. Reuters witnesses estimated up to 1,500 people entered Veracruz. Organizers of the caravan put the figure at 2,000. About 3,000 people were in the caravan when it set out, though some estimates since then have put the number higher. Overnight, the caravan stopped in the municipality of Jesus Carranza on Veracruz"s border with Oaxaca. Hector Martinez, a senior INM official, denied that authorities were trying to block the caravan"s progress, but again urged its members to accept documentation to stay in Mexico. The bulk of the people in the caravan are Central Americans, as well as people from the Caribbean who are seeking to escape economic malaise and security problems in their homelands. Organizers of the group said a new caravan with more Haitians could depart from the southern Mexican city of Tapachula on Thursday. A decision would be made on Wednesday about whether to set off, organizer Luis Garcia Villagran said.