The Irish Green Party, which had strongly opposed Mr Trump's visit, described the cancellation as "erratic".
Mr Trump was expected to visit his golf course in Doonbeg, County Clare, and Dublin on the weekend of 10-11 November. "The US side has cited scheduling reasons". However, widespread reports emerging this afternoon suggest that he has cancelled the visit.
A meeting has taken place today at Government buildings, between officials of both governments, and the visit has now been cancelled due to "scheduling reasons", according to a government spokesperson.
The Trump administration announced last month that the president would continue on to Ireland following the November 11 ceremonies, to "renew the deep and historic ties" between the two countries.
U.S. President Donald Trump's planned November visit to Ireland has been postponed, the Irish government said Tuesday, though the White House said only that the trip was up in the air. "As details are confirmed we will let you know".
Make sure you vote or I will be impeached, Trump warns supporters
At the rally, Trump railed against Democrats engaged in a mock conversation, playing both the role of supporter and defender. Jon Tester, who is up for re-election this year, for releasing allegations that derailed the nomination of Rear Adm.
He had been due in Ireland the following day.
Varadkar said then that Trump's decision to accept an open invitation "came a little bit out of the blue".
He added that the Irish government disagreed with Trump administration policies on climate change, migration, trade and other issues.
Green Party leader Eamon Ryan said: "Trump's positions and demeanour on every issue of the day, from climate to women's rights, from global relations to political decency, represent the opposite of Irish values".
Labour Party leader Brendan Howlin tweeted that Trump "has been no friend of democracy or human rights".
Irish Deputy Prime Minister Simon Coveney said last week that the visit "will be controversial, because everything Donald Trump does these days is controversial".