Nottingham City Council came under fire for the original adverts, which warned shoppers money given to beggars would "go up in smoke".
Thousands of people signed a petition against the posters for "vilifying" the homeless and dozens were torn down or defaced.
The new campaign features altered wording and urges donations to charity.
A second phase of the campaign had always been planned, the council said.
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The first set included messages such as "begging: watch your money go to a fraud" and "watch your money go up in smoke".
Punk-rock band The King Blues received thousands of likes and hundreds of comments on their Facebook page when it said the council was using money saved from closing hostels to "demonise the homeless".
Lead singer Itch said: "These posters... aren't saying here are homeless shelters you can donate to or some food banks where you can buy extra tins - they are just vilifying."
Nottingham City Council now said it has taken on board the reaction to the posters and altered the message, although the first batch remain on bins across the city.
The new larger posters now include details of how to give to charity and warn shoppers that "people who beg often have serious drug or alcohol problems".
A spokesman said: "What we have done following feedback from the public is alter some of the wording on the second batch to make clearer how people can donate to homeless charities.
"There is no additional cost involved because the designs were changed before they were sent to the printers."
Andrew Redfern, chief executive of Nottingham homelessness charity Framework, said the new posters were "factual" and gave more specific advice about donating to charity.
He did not personally think the old posters demonised homeless people.
"I didn't see it like that myself but I think it's better if we can keep people on board with the message we are trying to put across, and that is there are better ways to help people who are begging or sleeping rough or whatever it might be than by giving money directly to them," he said.
A series of anti-begging posters criticised for "demonising" homeless people have been reworded.