Organisers said while they were not opposed to gay or lesbian rights, they want to defend family values and the institution of marriage.
The demonstrators have called for a meeting with President Enrique Pena Nieto to debate the issue.
Mexico is a predominantly Roman Catholic nation, where public opinion has been divided since May, when Mr Pena Nieto announced plans to change the constitution.
Same-sex marriages are legal in some Mexican states, but Mr Pena Nieto wants it to be allowed across the country.
Last year the supreme court declared that a ban on such unions imposed in many of Mexico’s states was unconstitutional however, many state legislatures have not changed their statutes to comply.