West, a Tea Party favorite elected in 2010, said in a statement his legal team "does not believe there are enough over-counted, undercounted or fraudulent votes to change the outcome of the election," NBC News reported.
In the 14 days since Election Day, West had raised questions about possible inaccuracies in the results.
West said he would "take no further action to contest the outcome of this election," despite many unanswered questions, NBC News said.
Murphy, who was in Washington last week for orientation, held about a 1,900-vote lead after a partial recount.
"We're going to move ahead and we wish Congressman-elect Murphy very well, but I think that now is not the time to draw the process out," West said on Fox News.