Lawmakers from both conservative parties in the German coalition urged Chancellor Angela Merkel and her interior minister on Monday to resolve an internecine dispute over migrant policy that has thrown her three-month-old government into disarray.

However, Interior Minister Horst Seehofer refused in an interview published on Monday to change course, making a personal attack on the chancellor with whom he has long had a fractious relationship.

Seehofer offered to quit his cabinet post and the chairmanship of Bavaria's Christian Social Union (CSU) at a party meeting on Sunday.

The CSU had threatened to impose new controls at the German border this week if they deemed that agreements Merkel brought back from a European Union summit were insufficient to ease the migrant burden.

Merkel is deadset against unilateral action by the authorities in Bavaria, the main entry point for migrants into Germany, saying it goes against European law.

Merkel's Christian Democrats (CDU) rely on the CSU to maintain power through a coalition, also including the centre-left Social Democrats, formed just three months ago.

The two centre-right parties have been in an alliance for 70 years under which the CDU left the CSU to fly the conservative flag in Bavaria. However, the CSU now faces a strong challenge from the far-right Alternative for Germany (AfD) in October when the southern state votes in regional elections.

At a joint meeting of the CDU and CSU parliamentary groups, a chorus of lawmakers urged Merkel and Seehofer to make up.

Senior CDU lawmaker Volker Kauder said he expected a solution to be reached this evening. "We will stay together," he said to several minutes of applause, according to participants.

CSU hardliner Alexander Dobrindt said the problems were 'solvable' and reminded lawmakers of the value of their alliance.

Addressing the meeting, Merkel acknowledged that the desire to settle the dispute was great and vowed to do everything possible to get an agreement, people at the gathering said.

But Seehofer seemed to resist the pressure, suggesting that Merkel managed to remain in office after federal elections in September only thanks to his support.

While Seehofer was the one who threatened to resign, he accused Merkel of trying to force him out. "I will not let myself be dismissed by a chancellor who is only chancellor because of me," he told the Munich-based daily Sueddeutsche Zeitung. "The person I put into the saddle is throwing me out... I'm being asked to change course, but I cannot."

Upper Hand

Earlier, veteran CDU lawmaker and former finance minister Wolfgang Schaeuble warned that the conservative bloc was standing on the edge of abyss and called for them to agree.

This crisis is the latest sign of a divide across the EU between those who want to maintain open borders and those who want to restrict the number of migrants entering the bloc.

Seehofer was persuaded by party colleagues to talk to Merkel one last time on Monday, declaring he would make his final decision within three days.

For now, Merkel seems to be in the stronger position.

Her CDU lawmakers are still behind her while the CSU has baffled voters and commentators by backing themselves into a tight corner. A Forsa poll showed that 67 percent of Germans thought the behaviour of Seehofer and the CSU was irresponsible.

By letting the CSU tear itself apart over its future in the coalition, Merkel may yet rid herself of a formidable foe in Seehofer - as she has with a string of other top conservatives in her 12-1/2 years in office.

Bad blood between the two runs deep.

Seehofer, 68, has been a headache for Merkel, especially over her open-door migrant policy, and the last three years have been punctuated by a series of showdowns between the two.

He told colleagues on Sunday he saw no alternative to turning migrants back at the border despite Merkel's efforts in Brussels last week and that discussions with the chancellor had been fruitless, according to a party source.

If the row is not resolved, the CDU-CSU alliance may break up, robbing Merkel of her parliamentary majority. This could see her trying to lead a minority government.

Merkel would be only two seats short of a majority in the Bundestag lower house and may choose to rely on the Greens or pro-business Free Democrats to back her on individual policies.

She could also call a vote of no confidence, which she may win or which may trigger a new election. Opinion polls suggest the AfD would be among the biggest winners in any fresh vote.

Even if Merkel, once Europe's most powerful leader, limps on as chancellor, the bitter dispute is a sign that her authority is waning, say experts.