Conservative Chancellor Friedrich Merz, citing the threat of a hostile Russia, has tasked Pistorius of the centre-left Social Democrats with boosting recruitment to build up "the strongest conventional army in Europe".
But the question of how to get there has led to angry recriminations, as Pistorius prefers a purely voluntary approach and Merz's CDU/CSU has advocated the potential use of a draft lottery if necessary.
The coalition government had planned a first reading of a compromise draft law this week, but disagreement on the details sparked a row on Tuesday.
Pistorius told reporters on Wednesday that the idea of a draft lottery was a "lazy compromise" and would be too time-consuming in practice.
Some lawmakers from Merz's centre-right CDU/CSU reacted furiously to Pistorius's stance.
"In 30 years in parliament, I have never seen a minister torpedo an important bill and plunge his own MPs into chaos like this," senior CDU lawmaker Norbert Roettgen told the SĂĽddeutsche Zeitung.
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NATO targets call for Germany to build up its total military strength to 460,000 troops -- made up of 260,000 active soldiers and 200,000 reservists.
But the Bundeswehr is currently a far cry from those figures, with around only 182,000 active soldiers and 49,000 reservists.
Pistorius hopes to avoid the need for the draft by attracting more volunteers with better pay and benefits like free driving licences and technical training opportunities.
The row over conscription is not the only point of tension between the CDU/CSU conservatives and their junior coalition partners the Social Democrats.
Pistorius has also taken aim at CSU leader Markus Soeder, who has called for an aggressive response to suspected Russian drones that have been spotted over various sensitive sites in Germany.
After mystery drones shut down Munich airport this month, Soeder, who is also the state premier of Bavaria, advocated a drone response policy of "shooting down rather than waiting".
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Pistorius dismissed such talk as "gunslinger rhetoric" in comments to the Pioneer website.
"That sort of talk might work at high noon in Dodge City, but not in international politics where we need to prevent wars and avoid escalation."
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