The decision came after Trump, whose hardline immigration policies appealed to many GOP primary voters, met Saturday with his Hispanic advisory council and said in an interview Monday morning that he wants to "come up with a really fair, but firm" immigration policy.
Trump denied in an interview Monday morning on Fox News that he was "flip-flopping" on the issue of illegal immigration. And he told Fox News' Bill O'Reilly on Monday evening that Presidents Obama and George W. Bush had both used current law to deport some undocumented immigrants.
"Lots of people were brought out of the country with the existing laws. Well, I'm gonna do the same thing," Trump said. "We want to do it in a very humane manner."
Trump's new campaign manager, Kellyanne Conway, explained the decision to postpone the speech in an interview on "Fox and Friends" on Tuesday, suggesting she was still grappling with decisions made before she took the reins of the campaign.
"We inherited this schedule," Conway said -- though it was Conway herself who labeled this week "immigration week" for the campaign in an interview with CNN last Thursday. She added, "Although I think it's a great idea to have that kind of speech and certainly put together full plans, immigration is such a complex issue and Mr. Trump has been taking the counsel of many different people on this."
Trump also said in response to a question that he would not put undocumented immigrants in detention centers.
A Trump campaign source said the campaign decided to push back Trump's immigration speech as it is still fine-tuning its immigration policy and the speech's language.
As Trump prepares to wade once more into the heated immigration debate, the campaign is taking care to craft the critical speech, which the campaign absolutely wants to get right, the source said.
Lydia Blaha, the spokeswoman for Trump's Colorado campaign, also confirmed to CNN that Trump will not deliver a speech in Colorado on Thursday.
It is unclear when he plans to give the speech.
Speaking to CNN's Brianna Keilar on Monday, Alabama Sen. Jeff Sessions, a longtime ally of Trump's, emphasized that "there's not going to be mass round-ups and that kind of thing" in the Republican nominee's immigration plan. He added that the most important thing for Trump to accomplish is to "stop the lawlessness."
Sessions was also interviewed Tuesday on "New Day" on CNN, and appeared to equivocate about Trump's immigration position.
Asked if Trump had changed his position on the feasibility of a deportation force, one of the more controversial parts of Trump's past rhetoric on immigration, Sessions said: "What we're going to do is he's going to look at that and make a statement about that."
Trump on Monday visited a Fraternal Order of Police chapter in Ohio and is set to deliver a law-and-order-themed speech Monday night in the state.