President Md Abdul Hamid received him at Shahjalal International Airport.
The 80-year-old pontiff is the first pope to set foot in Bangladesh in 30 years. Pope John Paul II visited Dhaka in 1986.
Pope Francis headed to the National Memorial in Savar to pay tributes to the 1971 Liberation War martyrs.
He then visited the Bangabandhu Memorial Museum in Dhanmondi before heading to the Bangabhaban where he had a private meeting with Hamid.
Housing and Public Works Minister Mosharraf Hossain, Liberation War Affairs Minister Mozammel Huq, and top military and civilian officers greeted the pope at the memorial.
He stayed at the memorial for a little over 25 minutes. A contingent from the three forces gave him salute.
Pope Francis observed a minute’s silence in remembrance of the martyrs.
He also signed the visitors’ book and planted a tree at the memorial.
Bangabandhu Sheikh Mujibur Rahman’s daughter Sheikh Rehana and her son Radwan Mujib Siddiq guided the pope during his visit to the Bangabandhu Memorial Museum.
At the presidential residence Bangabhaban, the pope also met Cabinet members and diplomats at the Darbar Hall.
He later went the Vatican embassy in Baridhara for an overnight stay.
During his visit to Myanmar, the pope made no direct reference to the plight of the Rohingya Muslims to avoid a diplomatic incident with a Buddhist-majority country some have accused of ethnic cleansing.
He has again avoided the term ‘Rohingya’ in his address to an event with President Hamid hours after his arrival.
He instead spoke of “refugees from the Rakhine State”.
On the second day of his tour, he will lead a Mass at a rally at Suhrawardy Udyan. Later, he will hold talks with Prime Minister Sheikh Hasina at the Vatican embassy.
Later in the day, the pope will hold a meeting with bishops at Ramna Cathedral in Kakrail and attend an Interreligious and Ecumenical Meeting for Peace there to preach communal harmony.
Vatican spokesman Greg Burke, briefing reporters on the trip on Nov 22, said ‘a small group’ of Rohingya refugees will be present at the meeting for peace.
He gave no details of how they would be chosen, according to Reuters.
The event was not on the original schedule of the trip.
In the afternoon, he will attend a session to exchange views with the youths at the Notre Dame College.
He will leave Dhaka at 5pm Saturday after being seen off by Foreign Minister AH Mahmood Ali at the airport.
Catholics make up a tiny minority in Bangladesh.
Born as Jorge Mario Bergoglio in 1936 at Buenos Aires, Pope Francis ordained priesthood in 1969. He is also the first from the Americas, and the first from the Southern Hemisphere.
Defending the pope on not using the word ‘Rohingya’, the Vatican said on Wednesday that his moral authority was unblemished and that his mere presence drew attention to the refugee crisis, Reuters reported.
But a Vatican media call in Myanmar’s Yangon to wrap the pope’s visit only served to highlight the diplomatic minefield that the issue had presented for Francis.
According to Vatican spokesman Greg Burke, the pope's decision not to refer to the Rohingyas did not take away from anything he has said in the past - he had mentioned them and their suffering before his Myanmar visit - but added that Vatican diplomacy was "not infallible" and others were entitled to their views.
Muddying the waters for the Vatican delegation, a Myanmar regional bishop cast doubt at the same news conference about allegations of ethnic cleansing, suggesting "other communities" might be responsible for stoking them, according to the Reuters report.
"When we speak of the truth, we should go to an authoritative source or a reliable source to get the news ... Those who criticise should go to the scene to study the reality and history,” it quoted Bishop John Hsane Hgyi as saying.