Training camps abroad can be crucial in acclimatizing athletes for Rio de Janeiro's tropical conditions, but they are rapidly becoming unaffordable after the ruble lost almost half of its value against the U.S. dollar in the last 12 months.
With the ruble's value low and the Sports Ministry's budget facing cuts, athletes should stay in Russia rather than train abroad "in order to spend less of the currency reserves," Russian agency R-Sport quoted Nagornykh.
Officials will select priority sports and athletes for scarce funding, Nagornykh said. The financial problems "test everyone's professionalism," he added.
The measures affect athletes preparing for the Rio Olympics and the 2018 Winter Olympics in Pyeongchang, South Korea, he added.
Nagornykh's comments come almost a year after Russia topped the medal table at home in the Sochi Winter Olympics, following lavish preparations which outstripped any previous Russian Olympic effort, with entire teams of athletes sometimes based abroad for months.
During that time, Russia also invested heavily in training facilities at home, especially for winter sports, which will be useful in the drive to cut costs, Nagornykh said.
"Thank God, in the last five to six years, we very seriously updated our arsenal of training bases," he said, adding that performance standards would be maintained.
"Everything that's been planned that, without which we won't be able to prepare the teams for the Olympic Games in Rio and Korea, will be provided by the ministry, the federations, and in co-operation with the Russian Olympic Committee," he said.