Incumbent Democrat Bob Casey and Republican challenger Dave McCormick are now separated by about 34,000 votes.
With 98% of the expected vote in, McCormick leads by just over half a percentage point. Any statewide race in Pennsylvania decided by half of a percentage point or less is automatically subject to a recount.
McCormick declared victory after the Associated Press projected him the winner last week. ABC News has not yet projected a winner.
But Casey campaign officials said Monday the remaining votes to be counted could still tip the race in his favor.
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"Our county election officials will finish counting those votes, just like they do in every election," Casey said in a statement on Tuesday. "The American democratic process was born in Pennsylvania and that process will play out."
Any statewide recount must be ordered by the secretary of the commonwealth by November 14.
McCormick invited to Senate orientation
Senate Majority Leader Chuck Schumer did invite McCormick to attend a new member orientation on Capitol Hill Tuesday.
Republican senators were protesting earlier this week that McCormick was excluded from orientation week by Schumer because there are still uncounted ballots in his race.
Schumer's office had said it is custom to wait until all the ballots are counted but has since invited McCormick.
"I'm excited to be here. I'm glad I've been invited to the orientation, and I'm excited to get to work to bring about the change the people of our great Commonwealth of Pennsylvania have demanded," McCormick said.
Deadline to fix mail-in, provisional ballots
Meanwhile, Tuesday is the deadline for voters with problems with their mail-in and provisional ballots to get them fixed.
Election workers in Philadelphia have flagged thousands of provisional ballots that need ID verification. Other counties have hundreds more.
And all of these votes in limbo matter because of how close the Pennsylvania Senate race is.
RELATED: Deadline for mail-in, provisional ballots to be verified | Check ballot status
In order for your vote to be counted, you need to submit proof of identification to the board of elections.
The deadline for most options was 5 p.m. Tuesday, but you can still submit your form via email until 11:59 p.m.
For more information, visit this page at Phila.gov.