A new report on Russian sport is to be released on December 9.
Rune Andersen, who delivered a report to the IAAF's ruling council on Thursday, said his team would return to Moscow in January, after Canadian law professor Richard McLaren delivers his final report into Russia's doping programme, and report back the following month.
"This is a very important moment in the history of our sport", said Coe, who took office in 2015 after the selection held during the world championships in Beijing.
IAAF argues the change will quicken the punishment of cheats, remove opportunities for favoritism and corruption.
The reinstatement conditions demand that RusAF comply in full with the World Anti-Doping Code and IAAF anti-doping rules, that the IAAF and the Russian Anti-Doping Agency (RUSADA) are able to conduct their anti-doping programmes and testing without interference, and as a result the reintegration of Russian athletes into global competitions will not jeopardise the integrity of those competitions.
Track and field's governing body says its commercial agreement with sponsor Adidas will end this year, three years early.
Meanwhile, Japanese footwear and sports equipment manufacturer Asics has been named as an official partner of the IAAF, just a day after Adidas cut short its deal.
But it has withdrawn in the wake of an unprecedented corruption scandal that has seen senior former IAAF officials implicated in widespread bribery to keep quiet on positive tests by Russian athletes.
A special IAAF Congress will vote on Saturday on the reforms that Coe has championed. "Clean athletes have to know that we are in their corner".
Open balloting made it possible to identify the 10 countries that voted "No, ' making them look isolated in the sea of 182 'Yes" votes.
A remaining obstacle to Russia's reinstatement is convincing Andersen's taskforce that anti-doping officers will be allowed to do their work there. The IAAF said the unit's annual budget of US$8 million (7.5 million euros) will double what it now spends on anti-doping. She was accepted under IAAF rules because she was based in the US for several years, away from the Russian drug-testing system and its officials and lab staff accused of covering up hundreds of failed tests. "This would not have taken place had we not taken the tough decision we did previous year".
"Too much power rested in the hands of too few people", Coe said.