MOSCOW — Seven people died in a suicide bombing, including a respected Muslim cleric, and a border guard shot to death seven of his fellow soldiers before being killed on Tuesday in separate attacks in the Republic of Dagestan in the North Caucasus, where Russia has long battled violent Islamic separatists.

Even for Dagestan, where violence has become relatively commonplace, it was a shockingly bloody day.

The killings also coincided, jarringly, with a visit by President Vladimir V. Putin to the Republic of Tatarstan, where he honored the victims of recent attacks by Muslim extremists and insisted that terrorists would be defeated.

“Terrorists and militants of all kinds, whatever ideological slogans they hide behind, always act cynically, behind one’s back, and have only one aim: to sow fear and mutual hatred,” Mr. Putin said in a speech in the ancient town of Bolgar, a Muslim spiritual center. He added that “criminals will never achieve their despicable goals.”