The firefight erupted last evening after officers entered Nablus's Old City, a densely populated warren of alleyways that was one of the flashpoints of the second Palestinian uprising between 2000 and 2005.
The shooting was still continuing on Friday morning, security forces spokesman Adnan al-Damiri said.
Nablus governor Akram Rajub said that two police had been killed in the operation as well as two gunmen, both of whom he said were on a police wanted list.
Under the 1993 Oslo accords with Israel, Palestinian police are only authorised to operate in 18 percent of the occupied West Bank, encompassing most of the major Palestinian towns, including Nablus.