Leutheusser-Schnarrenberger, of the liberal Free Democratic Party, the conservatives' junior coalition partner, sided at the weekend with opposition parties in calling for more rights, even full marriage recognition, for gay couples.
But senior lawmakers from Angela Merkel's Christian Democratic Union and its Bavarian sister party the Christian Social Union have knocked back the calls.
“There are differences between marriage and equal rights for same-sex partnerships. And those must be reflected in the law,” the CDU-CSU deputy parliamentary leader Günter Krings told the daily Neue Osnabrücker Zeitung.
The CSU's own parliamentary leader Stefan Müller told the same paper: “In the Christian-liberal coalition, there are no plans to put partnerships of lesbians and gays on completely par with marriage.”
He added that the conservatives would “not make something the same that isn't the same.”
“The state protects marriage – that between a man and a woman – as well as families in special ways because the family is the nucleus of our society.”
Leutheusser-Schnarrenberger said on Saturday she favoured complete equality for gay couples but added that “A more socially liberal approach cannot be forced but must be achieved through patient argument.”
Since 2001, Germany has had “registered partnerships” for same-sex couples, which give them many but not all the rights of married straight couples. They do not, for instance, enjoy the same income tax advantages nor the right to adopt.
Last week, the environmentalist Greens called for full gay marriage to be allowed, while the centre-left Social Democrats called for registered partnerships to carry the same benefits as marriage.