"The treaty was signed yesterday. Its temporary application started yesterday and, of course, all Crimean residents who applied to the Federal Migration Service will get passports," Xinhua quoted Konstantin Romodanovsky as saying on Wednesday.
"This work has started. Some of the passports were issued today."
Without elaborating how many people have applied for Russian passports, he voiced belief that the intensity of issuing documents would grow each day.
Romodanovsky also said Russia was concerned by symptoms of a growing "humanitarian catastrophe" in Ukraine.
"As a sign, the number of elderly people and children entering Russia has grown twofold," he said, adding that the number of Ukrainians crossing the Russian border without any clear purpose was also increasing.
He did not give exact figures or periods of which he was comparing.
"This only strengthens our fears," Romodanovsky said, noting that the FMS has shared those concerns with the UN High Commissioner for Refugees about the worsening humanitarian situation in Ukraine.
Russian President Vladimir Putin on Tuesday signed the treaty with leaders of Crimea to accept the Republic of Crimea and the city of Sevastopol as part of Russian territory.
Crimea, a Ukrainian autonomous republic, held a referendum on Sunday, with some 96.6 percent of voters opting for joining Russia.
The referendum capped months of political unrest triggered by the Ukrainian government's decision in November not to sign an agreement on broader European integration.
Crimea, home to the Russian Black Sea Fleet and historically part of the Russian Federation, was transferred to Ukraine in May 1954, then a republic of the Soviet Union.