The explosion occurred shortly after the convoy entered Gaza through the Erez crossing with Israel, a security source in the convoy said.
Welcomed back to Ramallah by applause from a crowd of dozens of people, including cabinet ministers, Hamdallah repeated a call to Hamas to hand over control of Gaza's police force and civil emergency services to the Palestinian Authority.
He had been expected to hold a number of other engagements before leaving.
TRT World 's Muhannad Alami has more on this attack from Ramallah.
Hamas said the attack was an attempt to damage Gaza's security and "deal a blow to efforts to finalise reconciliation" between the main Palestinian factions.
No group has claimed responsibility for the bombing, which Hamdallah describes as an "assassination attempt". More radical militants, inspired by the Islamic State group, also operate in Gaza.
The Hamas-run interior ministry in Gaza said several suspects have been arrested in connection with the explosion.
"Hamas is fully responsible for this cowardly operation that targets the homeland, reconciliation and unity", said Fatah spokesman and Revolutionary Council member Osama al-Qawasmi.
"Hamas opening an investigation is not enough", he said.
Mustafa Ibrahim, a Gaza-based political analyst, said there are "several sides who are benefiting from this explosion".
Hamas criticised Abbas' accusation, saying it "achieved the goals of the criminals".
Some even went as far as hinting that the explosion may have been staged by the PA to implicate Hamas and force it to relinquish control over the Gaza Strip. "They planted explosive devices two meters deep".
The visit came as reconciliation efforts between Hamas and Abbas' Fatah party falter. The two reached an agreement to form a national unity government in October after a decade of failed attempts and often bitter acrimony. The hands behind this crime are the same hands that killed Mazen Fuqaha (ed: "commander of Hamas military wing killed past year in Gaza) and tried to kill General Tawfiq Abu Naim".
But it's now hard to see how the Egyptians would be able to continue with their efforts, especially in wake of the war of words that erupted between Hamas and the PA after the explosion.
Hamdallah's government is recognised by the global community, while Hamas is blacklisted as a "terrorist organisation" by the European Union and the United States. It also cast a shadow over a special White House meeting where global donor nations were set to discuss the dire humanitarian situation in Gaza. Hamas has condemned Trump's recent moves to recognise Jerusalem as the capital of Israel, and to move the U.S. Embassy to the city. In the video below, the blast hits at the 42 second mark.