Israeli officials said in a statementthat Sweiti had refused to give himself up near the West Bank city of Hebron after troops surrounded the house.
"[Sweiti] refused and opened fire at the forces, who then used engineering tools in addition to firing at the building's exterior wall, in order to cause him to surrender. The terrorist continued to fire at the force, and was ultimately killed," the statement said.
Witness reports, however, contradicted the official Israeli line, saying no exchange of fire was heard prior to the demolition of the home.
The body was later handed over to relatives and local residents.
Israel's military said Sweiti was wanted for a number of attacks on Israeli vehicles and border guards from 1999-2004.
Hamas strongly condemned the killing, calling the Israeli security operation an illegal assassination.
"The assassination of this al-Qassam commander is a dangerous crime, which comes in the context of the occupation's determination to eliminate the forces of the resistance, and especially the al-Qassam Brigades in the West Bank," Sami Abu Zuhri, a Hamas spokesman, said.
An Israeli high court order has deemed the killing of Palestinian suspects not engaged in a firefight illegal. However, recent media reportshave indicated that, contrary to the court order, the Israeli military pursues a policy of assassinating prominent Palestinian fighters.
The last alleged assassination carried out in the West Bank by Israeli forces was in Nablus last December, when four members of Fatah's military wing were killed.
Killed 'without cause'
An independent investigation into the killingby B'Tselem, the Israeli human rights group, recently concluded that the soldiers could have arrested the Fatah members, and that the men were killed without cause.
At the time, Israel claimed the men resisted arrest and posed a threat to the soldiers.
Monday's killing appeared likely to aggravate an already tense situation in Israel and the Palestinian territories.
Palestinian protesters clashed with Israeli securityforces on Sunday after settlers were allowed to march into an Arab neighbourhood in East Jerusalem.
US efforts to restart the peace process between Israel and the Palestinians have also stumbled, with George Mitchell, the US envoy to the Middle East, so far failing to secure a commitment from the Israeli government to freeze the expansion of settlements in East Jerusalem.