All four were kidnapped by Hamas militants from the Nova music festival on October 7, the military said in a statement, adding the four had been taken to hospital and were in “good medical condition”.
Footage posted on social media by Israeli authorities showed Argamani in an emotional reunion with her father after her rescue.
Argamani was also seen smiling and speaking on the phone with President Isaac Herzog in footage aired on Israeli television.
Israeli army spokesman Rear Admiral Daniel Hagari said the operation took place in two separate buildings “in the heart of a civilian neighbourhood”.
“While under fire inside the buildings, under fire on the way out from Gaza, our forces rescued our hostages,” Hagari said in a televised statement.
An Israeli soldier was “critically wounded” in the operation, which took place around 11:00 am (0800 GMT), he added.
“The message this morning to Hamas is clear: we are determined to bring back home all the hostages.”
The rare rescue comes eight months into the war with Palestinian Hamas militants in Gaza.
During the October 7 Hamas attack on southern Israel, militants took 251 hostages, 116 of whom now remain in the Palestinian territory, including 41 the army says are dead.
The October 7 attack resulted in the deaths of 1,194 people in Israel, mostly civilians, according to an AFP tally based on official Israeli figures.
Israel’s retaliatory bombardments and ground offensive on Gaza have killed 36,801 people, also mostly civilians, according to the Hamas-run territory’s health ministry.
Earlier on Saturday the military said in a separate statement that forces were “targeting terrorist infrastructure in the area of Nuseirat”.
A Gaza hospital said Israeli strikes in central areas of the territory, including in Nuseirat camp, has killed at least 55 people up til now, with “tens of wounded people.”
Hamas said in a separate statement: “There are dozens of bodies of martyrs and wounded lying on the ground, in the streets, and in safe rooms.”
The group added that Israeli forces were engaged in a “brutal and savage aggression on Nuseirat camp”.
AFPTV video showed thick plumes of smoke billowing into the sky from several buildings in Nuseirat.
In recent weeks the military has carried out intense air and ground assaults in and around Nuseirat.
On Thursday, the military struck a school-turned-shelter run by the UN agency for supporting Palestinian refugees, also known as UNRWA, which the Al-Aqsa hospital said had killed 37 people.
Dr Tanya Haj-Hassan, a paediatric intensive care doctor with Doctors Without Borders, was quoted saying the emergency department at Al-Aqsa Hospital “is a complete bloodbath … it looks like a slaughterhouse”.
The Israeli military acknowledged it conducted the strike in the Nuseirat refugee camp that targeted the UN school, saying it killed 17 “terrorists” there.
The news agency Axios states that a US administration official confirms that the American hostages unit in Israel aided in the retrieval of the four captives in Gaza. US President Joe Biden will be set to speak about the subject later today in France.
In February, another rescue mission freed two hostages, but the health ministry in Hamas-ruled Gaza said heavy air strikes that accompanied that mission killed around 100 people in Rafah, southern Gaza.
Israel’s Prime Minister Benjamin Netanyahu says Israel operated “creatively and bravely” to rescue the hostages in Gaza, and that they “will not let up until we complete the mission and return home all the hostages – both those alive and dead.”
