Plea to Abbas
Hamas said it feared that opening the crossing would risks the lives of Hamas fighters and other Palestinian factions.
The protesters called on Mahmoud Abbas, the Palestinian president, to hold himself responsible for ending the crisis by opening the Rafah crossing as the sole official Palestinian gateway.
Palestinian medical sources said that at least 28 Palestinians of those stranded on the Egyptian side of Rafah have died since the beginning of June.
Of the 6,000 people believed to be stranded there 20 per cent are suffering from illnesses and diseases that require immediate and daily medical treatment, health workers say.
The Israeli government announced on Monday that it was to allow hundreds of Palestinians stranded in the Egyptian Sinai peninsula to cross back to the Gaza Strip through Karm Abu Salim.
The Palestinian emergency government confirmed that it had agreed to the Israeli-Egyptian offer.
Palestinians have been unable to cross back to Gaza through the Rafah border crossing, which Israel closed after Palestinian in-fighting left Hamas in full control of the strip.
The decision came a day after angry protests by the stranded Palestinians, who have complained of neglect at the hands of both the Egyptian government and the Palestinian emergency cabinet.
Sami Abu Zuhri, a Hamas spokesman, speaking to Al Jazeera on Monday, said: "Talking about opening Karm Abu Salim crossing targets the movement [Hamas] and all the resistance forces."
"This serves economic objectives for the Israeli occupation authorities and for some Palestinian Authority leaders."
Abu Zuhri said other solutions could be found to resolve the issue and that Hamas was willing to re-open the Rafah crossing.
Riyad al-Malki, information minister in Mahmoud Abbas' emergency government, blamed Hamas for keeping the Palestinians in Egypt.
Al-Malki and other ministers of the Fatah-aligned Palestinian president's government visited on Sunday the Palestinians who have been stranded in Egypt's Sinai Peninsula for nearly a month.
He said: "Hamas wants to keep the Palestinians suffering as long as possible and use it as a political gain."
The information minister met Palestinians in the Sinai cities of Rafah and el-Arish on Monday, telling them that they are considered "one of most important priorities of the new government", and promised that they would work to allow them to return home.
Demonstrators in el-Arish yelled at the visiting delegation, shouting slogans including: "We don't want Fatah or Hamas, we just want to get out of here."