"We are really happy to receive our friend, the President of Algeria, Mr. Tebboune, in the Kremlin," Putin said after their talks.
"Algeria is a key partner for us in the Arab world and in Africa," he said, adding Russia wanted to ramp up energy and military ties.
The two leaders signed a declaration on a "deep strategic partnership," among other agreements.
Tebboune said that Western pressure on Algeria would not have any impact.
"Foreign countries may put pressure on us today but this will never affect our ties," he told Putin.
Both stressed the Soviet Union's robust support for Algeria during and after its fight for independence from France in the early 1960s.
"Our ties never changed," Tebboune said. "Algeria has always supported Russia, he said in translated remarks.
"We must maintain our independence," Tebboune said, adding Russia has been providing his North African country with weapons to help it "maintain our independence in these difficult circumstances."
Tebboune's three-day state visit comes as Moscow's offensive in Ukraine stretches into a second year.
Amid ruptured ties with the West, Putin is seeking to bolster relationships with countries in Africa, Asia and the Middle East.
Meanwhile, Tebboune was due to visit France in June but the trip, initially planned for May, might reportedly be postponed again.
The French presidency said the two countries were discussing "a suitable date."