Linke (Left) party leader Gregor Gysi told the Süddeutsche Zeitung that the Irish decision came at a time of "cultural revolution" that would have been "unimaginable" just a short time ago.
"There can't be any more delays," Gysi said. "It's up to us to catch up."
He was joined in his call by Green party leader Simone Peter, who said that Germany must "finally match" countries like France, Spain, Great Britain and Ireland which allow gay marriage.
But Justice Minister Heiko Maas of the SPD said that it would "unfortunately be difficult to achieve" gay marriage in the present CDU-SPD governing coalition.
While the cabinet plans to suggest some further steps towards equality at this week's meeting on Wednesday, conservatives have historically been against full marriage and especially equal rights for gay couples to adopt.
"The question of gay marriage is a highly political one which we would have to discuss widely in the CDU and Christian Social Union (CSU, the CDU's Bavarian Catholic sister party) if there was cause for change," family policy spokesman and MP Marcus Weinberg said.
"We don't want a serious political question for the union to be wedged in halfway through the parliament."
The CDU is already facing pressure from within its own ranks to change, with the Federation of Gays and Lesbians in the CDU calling for the party to change its tune.
"The clear 'yes' in Ireland is a signal. In Germany, something has to change in our party, too," federation leader Alexander Vogt told Spiegel Online.
"Frau Merkel doesn't need to dash forward any more. She just needs to jump aboard the train."