Murphy, speaking during a news conference on Monday, said he's had a "good back and forth" and that he's hopeful that any issues can be resolved soon.
Assembly Speaker Craig Coughlin extended the deadline to Feb. 18, allowing the Senate to "complete its discussions and conclude negotiations with the Assembly and governor on revisions to the cannabis legislation."
The legislation would address Murphy's concerns that the state Legislature's bill doesn't penalize underage adults and children for using the drug.
"Voters overwhelmingly support the legalization of cannabis and we are taking every step necessary to assure legalization and decriminalization become law," Coughlin said.
"Significant progress has been made and we are hopeful that concerns raised will be able to be addressed. I remain optimistic an agreement will be reached and that fair and responsible legislation will be advanced which will facilitate A-21 and A-1897 becoming law," he added.