The campaign, launched by the socialist government, shows men embracing, with safe-sex slogans underneath.
At least 10 mayors have decided to remove the posters, questioning the campaign's morality but denying homophobic motives.
Health minister Marisol Touraine said she would fight back via the judiciary.
The posters, sent to 130 towns and featuring a range of men of different ages and races, have captions such as "With a lover, with a friend, with an unknown. Situations vary. And so do modes of protection".
Ms Touraine said the local bans were unacceptable. On Twitter she urged people to share the images, which, she said, was the best response against critics who wanted to censor them.
Critics have called the posters "provocative" and "against good values and morality".
Bruno Beschizza, the conservative mayor of Aulnay-sous-Bois near Paris, was among those seeking to block the images, but denied homophobia, saying he would have responded the same way if the posters had featured heterosexual couples.
The mayor of the western city of Angers, Christophe Bechsaid, said he had asked for the posters to be taken down but "only in the vicinity of schools and the route of school buses". He said residents had complained, particularly parents.
Conservatism is said to be on the rise in France, with right-wing politicians outperforming the left.
Ex-Prime Minister Francois Fillon, a Catholic known for his traditional values, is the frontrunner to be the centre-right's presidential candidate. He goes head to head with Alain Juppe in a run-off vote on Sunday.
When asked about the posters on Tuesday, Mr Fillon said did not consider the campaign to be very skilful and he understood why people might be shocked. However, he added that the fight against Aids was more important.
On Wednesday, Mr Juppe told a French radio station he would not have banned the posters.
French judges are considering a controversial decision by several conservative mayors to take down HIV-awareness posters featuring gay love.