Asked if it could happen before the summer, Spindelegger said: "If we have talked about it [by then], it would be OK."
This is a change of direction for the ÖVP leader, as he recently backed away from allowing gay couples to adopt.
Spindelegger was speaking three days after Austrian transgender artist Conchita Wurst won the Eurovision Song Contest. Her success has been welcomed by supporters around the world as a sign of increasing European tolerance.
The ÖVP leader did not specify which rights he was referring to, saying only that the government would look into what needed improving.
The Social Democrat leader in parliament Andreas Schieder has demanded that adoption rights for gay couples be improved. He also called for the right to in vitro fertilization for gay couples, and complete equality for marriage.
At present gay couples are allowed to have registered partnerships, but not get married, which is only allowed for straight couples.
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When asked what boundaries the ÖVP would set for gay rights, Spindelegger said "I have no boundaries to set."