Assuage
"He also promised to give lawmakers a second vote in a bid to assuage fears that Britain was being rushed into an attack."
Source: Huffington Post
Verb
1. to make (an unpleasant feeling) less intense.
2. to soothe, calm, or mollify: to assuage his fears; to assuage her anger.
I was reading an article posted on the Huffington Post's front page that detailed the British Parliament's refusal to commit the nation into another Middle Eastern conflict following supposed evidence that Syria's President Bashar al-Assad used chemical weapons on rebels. The US began to beat the drums of war earlier this week with initial reports that the White House was taking the legal steps necessary for military action in Syria, bringing the country into another conflict in that sector of the world. With the British government's refusal to join in, the US has lost a vital ally.
Assuage would work similarly as quell in any sentence, you could say you want to quell the rumors about your cat's demise or your health and both words would hold the same context.
