BERLIN—Chancellor Angela Merkel’s government rejected calls for it to boost public spending and retreat from its promise of a balanced budget amid mounting evidence of a slowdown in Europe’s biggest economy and the threat of recession across the Continent.

The government on Tuesday slashed its growth forecast to 1.2% from 1.8% for 2014 and to 1.3% from 2% for 2015. Separately, a measure of analyst confidence in the German economy fell into negative territory for the first time in nearly two years, the latest in a troubling...