Mehmet Oz’s lead in Pennsylvania’s U.S. Senate primary shrunk to under 1,000 votes on Monday as Allegheny and other Pennsylvania counties tallied provisional ballots and prepared for the all-but-certain prospect of an automatic recount.

In one of the most closely watched Senate primaries in the country, Mr. Oz led former hedge fund CEO Dave McCormick by 992 votes — of more than 1.34 million cast in the race — as of late Monday evening, almost a week removed from the primary election.

With the margin still so tight and both campaigns jockeying for any vote they can get before a likely recount, Mr. McCormick’s campaign asked the Commonwealth Court, in legal paperwork filed late Monday evening, to require Pennsylvania’s 67 counties to tally mail-in ballots that are missing a handwritten date on the return envelope.

There’s no official estimate of how many of these undated ballots exist across the state, but in Allegheny County, the county with the most registered Republicans in Pennsylvania, there are 42 GOP ballots that meet this criteria, election officials said.