Russia was banned from international athletics in November 2015 after evidence emerged of state-sponsored doping.
Russia was banned from international athletics in November 2015 after evidence emerged of state-sponsored doping and must clean up its act before being allowed to return to the fold.
But a new IAAF taskforce report says six key targets are not being met and Coe warned that if the situation has not advanced by the time the taskforce next reports in July, new steps may be taken.
"The history of our sport in the last year or so has been our ability to make tough decisions, so we're not going to demur from that," Coe said after an IAAF Council meeting in London.
"The taskforce will keep trying to make sure that progress is being made, but there will come a point where we have to say, 'OK, if this is not that complicated and the road map is very clear, we will have to review what the next stage is.'
"I'm not going to speculate, but if progress is not being made and the report next time says exactly the same thing, then we are going to have to look again at what we need to do here.
"We are determined to see this through. It is non-negotiable."
Coe, who did not specify what measures might be taken, said the taskforce had been "disappointed" by the lack of progress made by Russia since its last report in February.
He cited concerns about "testing, the ability to get hold of athletes' biological passport samples and ongoing issues around closed cities and the employment of coaches from a tainted system who are still plying their trade".
"There is no reason why better progress has not been made," Coe said. "RusAF (the Russian Athletics Federation) should be under no illusion at all.
"The criteria we laid is down is the criteria that stands. This is what we are working to."
Russia was barred from last year's Rio Olympics and will not be able to send a team to this year's World Championships in London in August.
But 12 individual athletes have been allowed to compete as neutrals.
Seven were added to the list on Tuesday, including world 110m hurdles champion Sergey Shubenkov and world high jump champion Maria Kuchina.
Coe announced the IAAF, world athletics' governing body, had abandoned plans to remove the 50 kilometres men's walk from the Olympic programme.
He also expressed confidence the World Championships will be safe, in light of this week's attack on the Borussia Dortmund football team and the terror attack in London last month that left five people dead.
"I know from the London years that security is something you don't publicly discuss," said Coe, who headed the organising committee at the London 2012 Olympics.
"There are no guarantees, but there are few other cities I would rather be in for a major championship."