Trump planned to travel to the Times building, spokeswoman Hope Hicks told reporters without elaborating.
The president-elect confirmed in a tweet the meeting was to take place, saying "The meeting with @nytimes is back on at 12:30 today. Look forward to it!"
Earlier, Trump said on Twitter he canceled the meeting after the newspaper tried to change the terms agreed upon. The Times said it was Trump who had tried to change the terms, wanting the entire meeting off the record.
Trump was slated to speak with editors, reporters, columnists and the newspaper's publisher, according to the Times. The meeting was expected to include Trump's chief of staff, Reince Priebus, Trump's daughter Ivanka, and top advisor Kellyanne Conway, the Times reported.
After Trump's Twitter rant, Clifford Levy, the Times assistant masthead editor, responded with one of his own, saying, "We did not change the ground rules at all and made no attempt to."
In a statement, the Times said, "We were unaware that the meeting was cancelled until we saw the President Elect's tweet this morning. We did not change the ground rules and made no attempt to. They tried to yesterday — asking for a private meeting and no on-the-record segment, which we refused to agree to. In the end, we concluded with them that we would go back to the original plan of a small off-the-record session and a larger on-the-record session with reporters and columnists."
On Monday, Trump met with representatives of the media, including Lester Holt, Charlie Rose, George Stephanopoulos and Wolf Blitzer.
—Reuters contributed to this report.
(Disclosure: Comcast is parent of NBC and CNBC.)