Party leaders were unable on Saturday to unify behind one of the 16 Democrats contesting the seat.
For the result to become official, it must first be certified by board commissioners.
Reports said Rangel was leading Democratic challenger state Sen. Adriano Espaillat by 994 votes as counting continued.
In a rally in Harlem, Rangel blasted his challenger for filing a new legal challenge to his seeming primary victory.
As counting continues, Rangel's reported margin of victory has shrunk from 6 points on Tuesday to 2.6, reports said.
Reyes was a former chairman of the House Intelligence Committee and a close ally of Minority Leader Pelosi.
Personal communications obtained by The Hill show Arizona state Sen. Kyrsten Sinema as a vocal opponent of intervention after 9/11.
Many in the African-American establishment are backing the white candidate, Rep. Gary Peters, over Rep. Hansen Clarke, who is biracial.
Reps. Marcy Kaptur and Dennis Kucinich will be on the primary ballot Tuesday, but only one will be left standing.
Few campaigns celebrate a 10-point deficit in the polls two months before Election Day, but Rep. Mark Critz's staff (D-Pa.) believes a new survey shows momentum swinging their way in a tough primary showdown with fellow incumbent Rep. Jason Atmire (D-Pa.). The congressional Democrats, who have been allies in the House, were pitted against one another after redistricting collapsed their districts.
Critz's deficit is a marked improvement over a January poll that showed Altmire with a 16-point lead, high name recognition and positive favorability rating. And Critz — who won his seat in a special election after the passing of Rep. Jim Murtha (D-Pa.) — believes his numbers will continue to improve once he has a better opportunity to introduce himself to the suburban Pittsburgh voters Altmire currently represents.
"When two-thirds of the voters don't know you, when two-thirds of the voters haven't been represented by you, this is a great place to start," said Critz spokesman Mike Mikus. "The fact is, Mark is a lot stronger in the district he represented than Jason Atmire is in his."
The redrawn district incorporates more of Altmire's current district than that of Johnstown, Critz's socially conservative and economically liberal base.