Updated

President Trump on Monday urged New York to re-run its June 23 primary election in the 12th Congressional District, which still hasn't produced a winner as thousands of mail-in ballots have been tossed or remain uncounted.

Trump's comments marked a further escalation of his rhetoric against universal, nationwide mail-in balloting, which the president has warned could bring about “greatest election disaster in history."

"I think you probably have to take the Carolyn Maloney race and run it over again," Trump said, during a relatively subdued White House press conference Monday.

Thousands of mail-in ballots have been invalidated in the contest, and both Republicans and election experts have said the situation could be a harbinger of a disastrous nationwide mail-in vote in November.

"This is a small race, and it's all messed up," Trump said. "It's a mess. Nobody knows what's happening. ... It's a total disaster."

He noted that the United States Postal Service (USPS) suffers from systemic mismanagement, and argued it's not "prepared" to responsibly handle a barrage of mail-in ballots.

"The post office loses money on every package it delivers, which is ridiculous," Trump remarked.

FOX NEWS ANALYSIS SLOWS SLEW OF MAIL-IN BALLOT ISSUES NATIONWIDE

Trump also pointed to a series of other mail-in ballot problems nationwide, including the news that Thomas Cooper, a mail carrier in Pendleton County, admitted to election fraud.

Monday's remarks were a continuation of the president's previous comments on the topic. Last week, the president tweeted out a dramatic local news report highlighting missing ballots during a test of the USPS' ability to handle mail-in ballots. The president also held up a Wall Street Journal article titled "New York's Mail-Vote Disaster," as well as a CBS News article titled "Vote-by-mail experiment reveals potential problems within postal voting system ahead of November election." He cited a similar piece in The Washington Post.

Fox News has obtained a copy of a recent USPS memo sent to employees detailing budget-related cutbacks. In the memo, the USPS says mail carriers may have to leave mail behind at distribution centers in order to make it on time to their delivery routes.

GOP DEFEATS TAXPAYER-FUNDED MAIL-IN BALLOTS IN FLORIDA

"One aspect of these changes that may be difficult for employees is that – temporarily – we may see mail left behind or mail on the workroom floor or docks (in P&DCs), which is not typical," the memo reads.

Mark Dimondstein, the president of the America Postal Workers Union, told Fox News that the changes are significantly slowing down mail delivery and that he is concerned about the impact it will have on mail-in ballots in November.

“Anytime the mail slows down, it's harder for the postal workers to serve the customers, whether it's a mail ballot or anything else," Dimondstein said. "So, again, we're just absolutely opposed to any effort to slow down mail, to delay mail. And that includes, obviously, for the ballots as well."

At the White House on Monday, Trump distinguished between nationwide, universal mail-in ballots and absentee balloting.

"Absentee ballots are great," Trump clarified. "They go through a process. You have to request them. But the universal mail-in ballots have turned out to be a disaster."

Separately, the president dismissed reports that New York prosecutors have broadened their probe into Trump, calling it an extension of previous unsuccessful efforts to oust him from the White House.

Earlier in the briefing, Trump touted his administration's coronavirus response. The president said positive coronavirus tests have declined 6% week-over-week, and hotspots have seen "slow improvements," including Arizona, Texas and Florida.

Nevertheless, White House Coronavirus Task Force Coordinator Dr. Deborah Birx said on Sunday that the pandemic is "extraordinarily widespread" in the U.S. -- an assertion that was backed up by the nation's top infectious diseases expert, Dr. Anthony Fauci, who said that Birx had been referring to the “inherent community spread” that is occurring in some states, stating: “When you have community spread, it’s much more difficult to get your arms around that and contain it.”

CLICK HERE FOR THE FOX NEWS APP