Paramedics resuscitated Adamowicz at the scene before rushing him to the hospital where doctors said early Monday he had survived an operation but was in a "very, very critical condition".
The suspected attacker, a 27-year-old with a criminal record, remains in custody after being arrested.
"Unfortunately we can not yet say that Paweł Adamowicz's condition is stable", Dr Jerzy Karpinski, director of the health department in Gdańsk's regional administration, told Radio Gdańsk on Monday morning.
This breaking news story is being updated and more details will be published shortly.
Adamowicz has always been considered a hate figure in far-right circles for his vigorous defence of migrants and LGBT rights, but no evidence has emerged that the attack was politically motivated.
Nearly seven hours after the assault, Stefaniak told reporters that "the patient is alive" - triggering applause - but added that the mayor remained "in a very serious condition".
A man is held on the ground by security personnel after he attacked the mayor of Gdansk during a charity event in Gdansk, Poland on January 13, 2019.
One eyewitness told broadcaster TVN that the man appeared "happy with what he had done".
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"Horrified by the brutal attack on Gdansk mayor Pawel Adamowicz", tweeted Frans Timmermans, a Dutch politician and leading European Union official.
The right-wing ruling Law and Justice party faced accusations from its critics that an atmosphere of hatred against Adamowicz and others liberal political opponents helped instigate the attack.
"Despite our political differences, I stand without question in solidarity with him and those close to him..."
He stressed, however, that the 53-year-old Adamowicz is a "relatively young, healthy person with no health issues" and that there is hope his body will cope and his condition will return to normal.
She insisted politicians in Poland need "greater responsibility for words, for deeds" because "there is no shortage of madmen on both sides" of the political scale. More than five hours after the attack there were no updates on his condition.
Pawel Adamowicz, mayor of the port city of Gdansk, was attacked with a sharp tool during a fundraising event in the city tonight. "Now we have to establish how was it obtained, was the accreditation in his name and was he really entitled to be there at that time?"
Interior Minister Joachim Brudzinski said the attack was "an act of inexplicable barbarism".
European Council president Donald Tusk, one of the founders of the Civic Platform movement also urged people to pray for the injured mayor.