HARRISBURG, Pa. (CBS/AP) — Pennsylvania’s secretary of state says they will have the “overwhelming majority” of ballots counted by Thursday. The commonwealth still has hundreds of thousands of ballots left to count as Democrat Joe Biden and President Donald Trump fought to the end for the White House.

“They’re coming in — we’re getting 10,000 here, 20,000 here. Counties are furiously at work and it’s looking like we’re ahead of schedule,” Secretary of State Kathy Boockvar told CNN on Thursday. “I’ve been saying that we’ll have the overwhelming majority counted by tomorrow, but it’s looking like we’ll have the overwhelming majority counted by today.”

Some of the state’s most heavily populated locales, including Montgomery and Chester Counties in the Philadelphia suburbs, reported finishing their tallies.

The counting continued in Philadelphia and in other counties throughout Pennsylvania two days after Election Day.

The Trump campaign and the Republican Party mounted several legal challenges to aspects of the vote count, contending, for example, that GOP election observers were kept too far away from the tabulation in Philadelphia, that some Democratic-leaning counties unfairly allowed people to fix technical problems with their mail-in ballots, and that mail-in ballots arriving after Tuesday should not be counted.

Trump scored one legal victory as intermediate state appeals court on Thursday granted more access to party and candidate observers, allowing them to get closer — 6 feet away — to election workers processing mail-in ballots in Philadelphia.

The city filed an appeal with the Pennsylvania Supreme Court, citing concerns over worker safety and the potential for intimidation.

Mail-in ballot counting was temporarily stopped in Philadelphia after the Trump campaign won the legal battle. Counting was paused for about an hour or so as a compromise was negotiated in large part by Pennsylvania state Sen. Sharif Street.

The Trump campaign had sued after complaining that its observer could not get close enough to election workers to see the writing on mail-in ballot envelopes, to ensure that the envelope contains a signature and an eligible voter’s name and address.

Ballots without that kind of information could be challenged or disqualified. A Philadelphia judge had turned down the Trump campaign’s complaint, saying that observers are allowed by law to watch, not audit.

It was unclear whether any of the legal challenges would make a difference to an eventual outcome.

Bob Bauer, a Biden campaign adviser, said the Trump campaign lawsuits don’t have any merit and are designed to spread misinformation, disrupt vote counting and confuse the public.

“It is to create an opportunity to message falsely about what’s happening the electoral process,” Bauer said.

Democratic Gov. Wolf accused Republicans of seeking to undermine confidence in the election results, and his elections chief said the state has acted legally and properly to ensure a complete and accurate count. More than 2.6 million mail-in ballots were cast, and there has been no report of fraud or any other problem with the accuracy of the count.

Appearing on “CBS This Morning,” state Attorney General Josh Shapiro — also a Democrat and seeking reelection in a race that has not yet been called — said the count “may be going a little slow, but it’s going very, very smooth.”

He added: “I recognize everybody’s on edge. … Everybody wants to know and the best thing we can do is get an accurate count and make sure that these legal votes are counted and that’s exactly what’s happening here in Pennsylvania.”

(© Copyright 2020 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)

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