Murphy will succeed the late GOP Representative Walter Jones Jr., who died in February after 24 years in Congress.
For Bishop the race was reportedly seen as a measure of popularity for Trump, who campaigned for Bishop on Monday in Fayetteville.
Later on Tuesday, Trump congratulated both Republican candidates in a series of tweets.
BIG NIGHT FOR THE REPUBLICAN PARTY. CONGRATULATIONS TO ALL!— Donald J. Trump (@realDonaldTrump) September 11, 2019
Greg Murphy is a big winner in North Carolina 03. Much bigger margins than originally anticipated. Congratulations Greg!— Donald J. Trump (@realDonaldTrump) September 11, 2019
Dan Bishop was down 17 points 3 weeks ago. He then asked me for help, we changed his strategy together, and he ran a great race. Big Rally last night. Now it looks like he is going to win. @CNN & @MSNBC are moving their big studio equipment and talent out. Stay tuned!— Donald J. Trump (@realDonaldTrump) September 11, 2019
Earlier on Tuesday, North Carolina voters took to the ballots to fill two vacant congressional seats - one due to an absentee-ballot scandal and the other because a US House member died in office.
Millions of campaign dollars have reportedly been spent in the south-central 9th district race between Bishop and McCready, according to AP. The election do-over was ordered after evidence of ballot fraud appeared last fall that benefited McCready's then-GOP opponent, AP reported.
In 2016, Trump won the district by 11 percentage points. According to the US-based media reports, citing political experts, the outcome of the race in the 9th Congressional district may reportedly suggest that Republicans are losing popularity alongside Trump, raising questions about the viability of the incumbent president and his party for 2020.