Those sentences marked a central argument in Trump's speech — one that German officials would deem flawed.

Despite growing anti-refugee sentiment in Germany, there appears to be little appetite there for Trump's proposed solutions: In a German poll in March, only 6 percent said they would vote for him if they could. Merkel has an approval rating of 47 percent.

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German officials also dispute claims that crime levels have increased because of the refugee influx last year. In an unusual move, Germany's Interior Ministry and the Federal Criminal Police Office released crime data for 2015 and the first quarter of 2016 in June. "Immigrants are not more criminal than Germans," a ministry spokesman was quoted as saying. Syrians, Iraqis and Afghans committed fewer crimes than refugees from other countries. Overall, crime levels have declined over the first quarter of the year, officials said.

It might be too early to gauge the full effect of the refugee influx on crime levels in Germany, and there are certainly issues that nobody can deny. There has been an increase in crimes motivated by religion or ethnicity — those numbers include brawls among asylum seekers and terrorism-related offenses. There has been a sharp rise in extremism, and there have been worrying incidents of mass sexual assaults.

Leaked police documents recently suggested that at least 1,200 women were sexually assaulted in Germany on New Year's Eve. Half of the identified suspects were recently arrived foreign nationals.

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Questions have arisen about why officials had not made those documents public, and police officials in Germany and elsewhere in Europe have been accused of trying to cover up crimes committed by refugees (authorities have denied the allegations). Criticism has also targeted media outlets, which are not allowed to specify the nationalities of criminals under Germany's press regulations.

For many Germans, the New Year's Eve incidents constituted a level of criminality previously unknown. But, overall, crime in Germany has not risen to "levels no one thought they would ever see."

Moreover, what Trump forgot to mention is that one of German authorities' biggest worries is the violent backlash against refugees from the far right. Hundreds of asylum centers have been burned down since last year, and refugees have been physically harmed in attacks. Those attacks have contributed to the increase in crimes motivated by religion or ethnicity, investigators say.

In April, German federal police warned that anti-refugee sentiments could escalate: "Apart from physical harm, one has to reckon with murders," authorities concluded. They also argued that neo-Nazis had fueled a "climate of fear," which had targeted journalists, pro-refugee volunteers and politicians, in particular.

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A more honest way of describing what has happened in Germany since early 2015 would be to note that some forms of crime have been on the rise, while others have decreased. The refugees most likely to come to the United States should Hillary Clinton be elected — namely, from Syria — have committed fewer crimes overall than other immigrants in Germany.

Including those numbers, however, would hardly have supported the argument Trump was trying to make.