The family of the late Sen. Frank R. Lautenberg, D-N.J., has endorsed Rep. Frank Pallone Jr. in next month’s special election Democratic primary.

“We are saying: Stick with Frank,” the family said in a statement released Monday by the Pallone campaign.

Pallone is facing three other Democrats in the Aug. 13 primary: Newark Mayor Cory Booker, Rep. Rush D. Holt and state Speaker Sheila Oliver. The winner will be heavily favored in the Oct. 16 special to fill the remaining year of Lautenberg’s term.

Lautenberg announced in February that he would not seek another term. He died on June 3, which led Gov. Chris Christie to call for a special election.

With the strongest name identification, Booker has held wide leads so far in public polling on the race. Still, the family’s decision not to endorse him is hardly surprising. Booker’s announcement that he was exploring a Senate bid before Lautenberg had announced his re-election plans set off party drama in the Garden State.

“Deciding which candidate to endorse was not an easy decision,” the family said. “Most of the candidates in the Democratic field have proven themselves as hardworking, progressive leaders who care deeply about New Jersey. But only one of them stands out as ready to continue Frank Lautenberg’s progressive leadership in the U.S. Senate. That candidate is Congressman Frank Pallone.”