By Joern Poltz

ST. QUIRIN, Germany (Reuters) - Germany must face the fact that Islamist terrorism has arrived and respond with tougher security and tighter immigration policies, Bavaria's state premier said on Tuesday.

"Each attack, each act of terrorism, is one too many. Islamist terrorism has arrived in Germany," Horst Seehofer, a long-standing critic of Chancellor Angela Merkel's open-door refugee policy, told a news conference.

"We need more security in Germany. People are riled up, full of fear, and that is completely understandable. They need reliable answers from politicians and not endless debates and justifications," Seehofer said after a meeting of party leaders.

A spate of attacks in Germany since July 18 have left 15 people dead - including four attackers - and dozens injured. Two of the assailants had links to Islamist militant groups, German officials say.

Two of the five attackers recently entered Germany from Syria, another was from either Pakistan or Afghanistan, stoking concerns about unprecedented immigration after 1 million migrants arrived last year, many fleeing conflict in the region.

Immigration and security are sure to be big topics in next year's federal elections, where the clash between Seehofer's Christian Social Union (CSU) and Merkel's Christian Democrats (CDU) may undermine conservatives' hopes of staying in power.

"TO THE EDGE"

Bavarian Interior Minister Joachim Herrmann told the news conference Germany should rethink rules that limit deportations of refugees for medical reasons, and significantly lower hurdles to deporting refugees who break the law.

"We must push it to the edge of the envelope currently permitted under European law, and we have to think about whether the EU rules have to be changed," Herrmann said.

The 27-year-old Syrian who blew himself up in the southern town of Ansbach on Sunday had been spared deportation due to medical reasons for over a year, but had recently been told he would be deported to Bulgaria.

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He had also been in trouble with police for drugs and other offences.

Bavarian officials said their state - the site of three of the recent attacks - would bolster police staffing and equipment, but would also push for federal restrictions on surveillance of potential suspects to be eased.

Federal Interior Minister Thomas de Maiziere, of Merkel's Christian Democrats, has said no changes would be made to changing asylum or immigration rules until investigations into the recent incidents are finished.

Authorities said there was no Islamist link in Tuesday's incident at a university clinic in Berlin, in which a 72-year-old man shot a doctor before killing himself.

The spate of violence in Germany followed the attack in the French city of Nice on Bastille Day, July 14, when a Tunisian killed 84 people by driving a truck into them, an act claimed by Islamists.

Islamic State also claimed responsibility for the latest attack in France, on Tuesday, where an elderly priest was killed in a church.

(Reporting by Joern Poltz, Erik Kirschbaum, Andrea Shalal, Michelle Martin and Hans-Edzard Busemann; Writing Michelle Martin; Editing by Andrea Shalal and Robin Pomeroy)