Moore faces Democrat Doug Jones, 63, a former US attorney, in a special election on December 12 to fill the Senate seat vacated by Jeff Sessions, now the USA attorney general.
Conway added that "Mr. Moore has denied that conduct", and "you've got other people out there talking about what did or did not happen many years ago", slippery phrasing that recalls her boss's classic rhetorical device "many people are saying".
Roy Moore is now losing to Doug Jones in the first major poll following the publication of harassment allegations. On Saturday, Moore, 70, said his opponents - Democrats and the Republican establishment - were "desperate" and wouldn't end his campaign.
Polling by Louisiana-based JMC accurately forecast voting patterns in the earlier round of voting in Alabama, where Moore captured the Republican nomination over Luther Strange, who had been appointed to fill the seat on an interim basis.
Over the weekend, more Republicans distanced themselves from Moore.
The Republican tweeted his decision Friday, joining Utah Sen.
The White House says Trump believes Republican Senate candidate Roy Moore "will do the right thing and step aside" if sexual misconduct allegations against him are true.
Despite pressure from top Republicans to drop out of the race following the allegations, Moore has pledged to stay in the race and disprove the accusations.
"There's a special place in hell for those who actually perpetrate these crimes, and I think Roy Moore has to do more explaining than he has done so far", White House Director of Legislative Affairs Marc Short told NBC's "Meet the Press" Sunday.