Palestinian Authority President Mahmoud Abbas on Tuesday rejected calls to halt peace talks despite the crisis in the Gaza Strip, and criticized Hamas for firing rockets at Negev communities. "Negotiations and contacts with Israel must continue," Abbas told reporters in Ramallah. "We must even step up these negotiations and contacts to end the suffering of our people." Abbas, who was speaking at a joint press conference with Dutch Foreign Minister Maxime Verhagen, said halting negotiations wouldn't help the Palestinians. "How can we persuade the other side that our people are suffering if we turn our backs and say no to negotiations with Israel?" he asked. "The talks must continue and we must reach an agreement by the end of this year that satisfies our people and meets their national aspirations. We want to reach an agreement on borders, settlements, refugees and Jerusalem," he continued. Foreign Minister Tzipi Livni, speaking Tuesday night at the Herzliya Conference, said that both Israel and the Palestinian Authority "must refrain from letting problems from the outside come into the negotiating room." Without referring specifically to recent Palestinian threats to suspend the negotiations because of the events in Gaza, Livni said that both the PA and Israel must resist the inevitable domestic demands - throughout the negotiating process - to suspend the talks because of events on the ground. Livni said it was obvious that Hamas's control of Gaza would have to be addressed. "Gaza is not somewhere there in the distant south," Livni said. "It is a problem that must be contended with." Israel must respond and would continue to respond to the terrorism from Gaza, she said. "I believe that Israel does not need to apologize for its existence, or apologize for protecting its citizens. It will protect its citizens even at the price of condemnation from the world." Abbas condemned the rocket attacks that, he said, gave Israel an excuse to impose a blockade and attack Gaza. He also criticized Israel's military operations in the Strip, saying such actions "hindered" the peace process. "We don't want to give an award to those who seek to undermine the peace process," he said. The PA president reiterated his readiness to assume control of the border crossings in the Gaza Strip. However Hamas did not want the Palestinians to lead a normal life, he said. Hamas leaders rejected Abbas's offer to take charge of the crossings and accused him of conspiring with Israel and the US to topple the Hamas government in Gaza. "The Palestinian Authority in Ramallah has played a major role in the blockade imposed on the Gaza Strip," said Hamas legislator Mushir al-Masri. "Until now, Hamas has not received an official request from Abbas to reopen the borders." The idea of PA control of the crossings, however, is gaining steam, having received support recently from the US, EU and UN, with the feeling being that this would give the Authority some kind of foothold in Gaza. Israel's official position, however, is that the PA is not ready to take over the crossings, and that its past performance at the border passages, before Hamas took over Gaza in June, did not give much reason to believe that the Authority was now in any better position to effectively control the crossings. Defense officials said there no chance that Israel would transfer control of the crossings into the Gaza Strip to the Palestinian Authority. "How can we give the PA control over the crossings while Hamas is in charge of Gaza?" one defense official asked. "It would be like giving Hamas the responsibility." Hamas spokesman Fawzi Barhoum lashed out at Abbas for criticizing the rocket attacks. "Abbas is involved in the blockade on the Gaza Strip," he said. "Abbas is colluding with the Israelis and Americans to increase the suffering of our people in the Gaza Strip." Barhoum also criticized Abbas for refusing to halt the peace talks, adding that the PA president was playing into Israel's hands and providing it with a pretext to continue its "aggression" against the Palestinians. Also Tuesday, Hamas said that Israel's decision to resume fuel supplies to the Gaza Strip was insufficient, and vowed to step up protests against the continued closure of the crossings. The Islamist movement expressed deep disappointment with the position of most Islamic countries regarding the latest crisis in the Gaza Strip. Yaakov Katz contributed to this report.