Varadkar will then go to New York for a number of "community, economic and cultural" engagements, including the site of the new Irish Arts Centre and the launch of the New York Washington Ireland Program.
"I actually think on this issue the majority of American people would agree with what I have to say, even if the administration doesn't".
The Taoiseach visited the museum dedicated to Mr Kennedy's assassination on the second day of his St Patrick's Day trade mission to the US.
Leo Varadkar has been asking US State governors how to deal with Donald Trump ahead of their meeting later this week.
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Mr Varadkar met the Republican governor and his wife Cecilia, who has Irish heritage.
Mr Abbott has been criticised by LGBT campaigners for his opposition to same sex marriage and his stance on a number of other social issues impacting the sector.
Mr Varadkar said there was a risk of gaps emerging between the European Union and America around issues such as tax and trade.
He officially thanked the Choctaw Nation, whose ancestors provided relief to Ireland during the Great Famine, saying Irish and Chochtaw people have a "sacred bond" binding us together.
On Tuesday, he'll travel to Washington DC, and deliver a foreign policy address to the Brookings Institution.More news: Trump eyes US$60 billion in tariffs on Chinese tech
That evening, the Taoiseach and Senator George Mitchell will be keynote speakers at a congressional event to mark 20 years since the signing of Northern Ireland's Good Friday Agreement peace agreement.
On Wednesday, Varadkar will meet representative of Irish companies succeeding in the US market and hold roundtable discussions with members of the US Chamber of Commerce to "promote Ireland as an investment location".
The Taoiseach says he is not apprehensive about the meeting, but has asked the pro-Trump governors of Texas and Oklahoma how to approach the U.S. president.
The Taoiseach will be guest of honour at a breakfast hosted by Vice President Pence on the morning of 16 March.More news: Plateau Imposes Curfew On Communities Where 25 People Got Killed