BERLIN — Angela Merkel met Wednesday with the leaders of three smaller parties for preliminary talks on forming a new government, amid mounting pressure on the German chancellor from within her own party following its poor result in last month’s election.

Hours after the first set of talks got underway, one of Merkel’s allies resigned as governor of Saxony, where the Christian Democratic Union came a close second behind the upstart Alternative for Germany, or AfD, last month.

Stanislaw Tillich, who has been in office since 2008, said he was handing over the reins because “new answers are needed.” Merkel’s party has governed the state since German reunification in 1990.

In Berlin, talks between Merkel’s Christian Democratic Union, its Bavaria-only sister party the Christian Social Union and the pro-business FDP were a good “first step” to sound each other out, FDP general secretary Nicola Beer told reporters in a short statement after the meetings.

Merkel’s bloc took about a third of the vote in September’s general election, the largest single share of any party — but without enough seats to govern alone.

Because the center-left Social Democrats have said they’re not interested in continuing the current “grand coalition” with Merkel, her Union bloc is holding separate talks with the free-market FDP and the environmentalist Greens. Support from both parties would be needed to form a majority government in parliament.

The parties haven’t entered into coalition at the national level before and their stance on migration, taxation and measures to combat climate change vary widely.

The Union bloc and the FDP have frequently teamed up to govern together in the past, and CSU general secretary Andreas Scheuer said bridging gaps with the Greens would likely be “a greater and more difficult component” to forming the coalition.

All four parties are expected to meet together for the first time Friday.

Forming a coalition will still likely take weeks, or even months, though Scheuer expressed optimism that the opening talks this week would bring the process “a large step forward.”