The network added that the adverts disparage its journalists and push unsubstantiated allegations of corruption against former vice president Joe Biden.
CNN’s decisions come as the Trump administration has escalated its attacks on congressional Democrats' impeachment efforts and continued to lash out at media organisations it tries to discredit as "fake news."
The move brought renewed ire from Mr Trump's re-election campaign, as communications director Tim Murtaugh called the news network a "Democrat public relations firm" that "spends all day protecting Joe Biden."
The ad accuses Mr Trump's potential 2020 opponent of corruption, continuing a favourite talking point of Mr Trump and his supporters amid an impeachment inquiry and concerns Mr Trump used his office to create trouble for a political rival.
The 30-second commercial claims that Mr Biden promised Ukraine $1bn (£810m) to fire a prosecutor looking into "his son's company."
Hunter Biden sat on the board of energy firm Burisma but does not own it and while Mr Biden was key in the Obama administration's efforts to remove Ukrainian prosecutor Viktor Shokin using US aid as leverage, no evidence indicates that Mr Biden sought to help his son. Widely criticised for his handling of corruption cases, Mr Shokin was eventually voted out of office.
The ad goes on to criticise another common Trump target, accusing "media lap dogs" of aiding Democrats' impeachment efforts. It depicts prominent journalists bashed by Mr Trump: CNN hosts Don Lemon and Chris Cuomo, White House correspondent Jim Acosta and MSNBC host Rachel Maddow.
CNN said in a statement that "in addition to disparaging CNN and its journalists, the ad makes assertions that have been proven demonstrably false by various news outlets, including CNN."
Mr Murtaugh maintained that the Biden ad is accurate and was "reviewed by counsel."
Another 30-second video titled "Coup" and released on Wednesday has been rejected as well, CNN said on Thursday.
"Coup" decries Democrats' impeachment efforts as an attempt to "undo the election regardless of facts" and attack Mr Trump "by any means necessary."
It also accuses representative Adam Schiff, D-Calif, chairman of the House Intelligence Committee, of fabricating evidence during a discussion of a whistleblower complaint against Mr Trump, a claim also broadcast from the president's Twitter account (Mr Schiff has said his paraphrase of Mr Trump's controversial call with Ukraine's president "was meant to be at least part in parody").
The impeachment push is "nothing short of a coup and it must be stopped," the Trump ad declares.
CNN cited similar concerns about false statements in declining that newer commercial, saying the spot makes claims about the whistleblower complaint against the president that the intelligence community inspector general has debunked.
"In addition, it is inaccurate to use the word 'coup' to describe a constitutionally prescribed legal process," the company stated, echoing critics who slammed Mr Trump's comparison of impeachment to an opposition group's violent, illegal overthrow of a government.
Mr Trump's re-election campaign did not immediately provide comment on CNN's decision about this second ad.
Another commercial submitted by Donald Trump for President, called "Changing Things," has been accepted, CNN said.
Networks have rejected presidential campaign commercials before. Last year, channels including Fox News – the president's favoured news network – nixed an ad that CNN and others called racist for its depiction of immigrants as "dangerous illegal criminals."
The Washington Post
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