Last month both companies' boards approved the proposed deal, which the companies said at the time valued the privately-held Presidio at about $101 million.
On Friday, BioCryst and Presidio said in a news release that that they decided that ending the proposed deal was in the best interest of both companies and their shareholders at this time.
Both companies' boards approved terminating the transaction.
The deal had called for BioCryst to issue 24.5 million shares of its stock to Presidio shareholders in exchange for all of their outstanding shares. It also included $25 million of new cash financing from some Presidio stockholders.
Presidio Pharmaceuticals is based in San Francisco, while BioCryst's headquarters are in Durham, N.C.
BioCryst shares finished at $1.60 per share on Thursday. They have traded in a 52-week range of $1.08 to $5.95.