World Athletics says it will expel the Russian Federation (Rusaf) as a member if it does not pay an outstanding fine and costs before 15 August.
A payment of $6.31m (£4.84m) for anti-doping breaches was due by 1 July.
But Russian Sports Minister Oleg Matytsin says the payment will be made before mid-August.
Failure to pay would see all Russian athletes, including those allowed to compete as neutrals, out of international competitions.
Russia's athletics federation was suspended in 2015 after a report commissioned by the World Anti-Doping Agency (Wada) found evidence of mass doping among track and field athletes.
Rune Andersen, chair of the taskforce overseeing Russia's reinstatement efforts, expressed his disappointment that they had seen "very little in terms of changing the culture of Russian athletics" in the past five years.
He said the taskforce had spent "an enormous amount of time and effort trying to help Rusaf reform itself and Russian athletics, for the benefit of all clean Russian athletes" but the response from Rusaf had been inadequate.
Any expulsion would have to be approved by the World Athletics Congress.
Earlier this week, former doping mastermind turned whistleblower Grigory Rodchenkov told BBC Sport that no Russian athletes should be allowed to take part in the postponed Tokyo Olympics next year.
Rodchenkov, who was behind Russia's state-sponsored doping scandal, said the country had not changed despite being banned from all major sporting events for four years in December for manipulating laboratory data.