Santos said: "There will be no tolerance for the kidnappings, harassment and terror carried out by criminal gangs."
"I will continue to cleanse these areas of the gangs who are robbing the people of their security."
He said gang members fired thousands of rounds at UN troops, who returned fire.
A UN spokesman said the organisation was now in charge of the Boston part of slum.
The raid was one of the biggest in months by peacekeepers, who were sent to Haiti more than two years ago to quell violence during the 2004 removal of Jean-Bertrand Aristide, the former president.
After the firefight, about 100 Cite Soleil residents staged a protest outside the UN military base in the slum, waving a white sheet and chanting "We want peace".
Damas Augustin, a protester, said: "We want this fighting to stop so innocent people of Cite Soleil can stop being victims and live as human beings."
In December last year, UN troops raided another part of Cite Soleil to break up a kidnapping gang.
The UN said six suspected gang members were killed, although residents said 10 people died and that all were civilians.