Germany's constitutional court ruled last week gay people should be allowed to adopt a child already adopted by their partner, and that the present ban was unconsitutional as it violated the principle of equal treatment.
"We will of course implement the constitutional court's ruling – that is called for now. At the same time, we will see whether tax amendments are necessary," Volker Kauder, leader of the CDU's parliamentary group, said in a newspaper interview.
At a party congress last December the CDU had thrown out a proposal to give same-sex couples the same tax perks as heterosexual couples.
The CDU's apparent change of heart was criticised by opposition Social Democrats, who accused it of being forced by the court into embracing reality.
The CDU has sought to boost its urban appeal ahead of a federal election in September by giving more prominent roles to women and ethnic minorities.
The CDU's sister party in Bavaria, the Christian Social Union, warned against urgent changes.
"There is no grounds for taking hasty action or even making an about face on the subject of equal rights for married couples and same-sex couples," said Gerda Hasselfeldt, head of the CSU's parliamentary group in Berlin.
Opposition parties and gay activists accuse Mrs Merkel's government of dragging its feet on equality for gay couples.