BERLIN — The German cabinet endorsed measures on Wednesday that would make it easier to deport many noncitizens convicted of crimes, responding to outrage over the sexual assault of hundreds of women by foreigners on New Year’s Eve and growing skepticism about the government’s ability to accommodate more than one million asylum seekers.

The legislation would lower the bar for denying criminals the right to stay in Germany, allowing the authorities to require anyone to leave the country if convicted of homicide, bodily harm, sexual assault, violent theft or serial shoplifting, even if given only a suspended sentence.

The measures require approval in Parliament, but Chancellor Angela Merkel’s coalition holds a majority there and they are expected to pass easily.

Ms. Merkel’s refusal to limit the number of migrants entering the country has damaged her popularity and caused a rift in her governing coalition.