The pope also told reporters that he would keep an open mind and not pass judgement on Trump until first listening to his views at their meeting on May 24.
"Even if one thinks differently we have to be very honest about what each one thinks", Francis said.
Pope Francis has said he will be "sincere" with Donald Trump over their sharp differences on subjects such as immigration and climate change.
In his social media rant, Trump also said that Pope Francis was being used as a pawn and that those who were doing so should be ashamed of themselves, especially when illegal immigration had become so rampant and lives were on the line.
"There are always doors that are not closed", he said. "We have to look for doors that are at least ajar, to pass through and speak of things we agree on and move forward from there".
The pope added that people should say what they think, but "with respect".
The Vatican's deputy secretary of state, Archbishop Angelo Becciu, had said in February there was "worry" over Trump's immigration actions, after Trump signed the first of two executive orders temporarily banning travel from a handful of Muslim-majority countries.
The two men also disagree strongly about climate change.
Trump has said he will make his decision on whether to stick to the agreement before the G7 meeting in Taormina, Sicily later this month.
Asked May 13 about the authenticity of the Marian apparitions, which reportedly began in 1981, the pope referred to the findings of a commission chaired by Cardinal Camillo Ruini, the retired papal vicar of Rome. "In our talk things will come out, I will say what I think, he will say what he thinks, but I never, ever, wanted to make a judgment without hearing the person".
That same day, Trump responded to the pope's comments during a campaign rally in SC, telling supporters he is "a good Christian".
The Pope seemed in part to be walking back a comparable conversation from a year ago, where another journalist caught him by using a similar subterfuge. "I can't do that", the pontiff said.
Trump, who is a Presbyterian, then said for a religious leader to question a person's faith is "disgraceful".
Trump will call on Francis mid-way through his first foreign trip, after visiting Saudi Arabia and Israel and before attending a North Atlantic Treaty Organisation summit in Brussels and a G-7 summit in Italy.
Thomas Williams pointed out in a Breitbart piece how Trump and the pope are actually coming into the meeting with common ground on numerous other issues besides the two Pope Francis was asked about on the plane.
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