Gaza demonstrators on Sunday demanded that Hamas secure the release of all its prisoners held in Israeli prisons, in a swap for abducted soldier Gilad Schalit, as Israeli protesters urged the government to be flexible, so that it could bring Schalit home after four years.Indirect negotiations between Hamas and Israel stalled at the end of last year. But thousands of Israelis in the last week have tried to jump-start the negotiations with their feet as they joined Schalit’s parents, Noam and Aviva, who on June 27 began an 11-day trek to Jerusalem.RELATED:Gaza families on Schalit: No prisoner exchange dealMashaal: Hamas won't back downMedia reports speculated that the issue of Schalit’s continued captivity in Gaza was the focus of talks held in Cairo on Sunday by Egyptian security chief Omar Suleiman, National Security Adviser Uzi Arad and Yitzhak Molcho, a senior adviser to Prime Minister Binyamin Netanyahu. Egypt has previously mediated between Israel and Hamas in the negotiations for Schalit’s release. The Prime Minister’s Office on Sunday night denied the reports.Earlier in the day, Gazans marched to the home of Hamas “Foreign Minister” Mahmoud Zahar and urged him to work for the release of all Hamas prisoners held by Israel.Netanyahu has offered to trade 1,000 terrorists, including 450 Hamas members, for Schalit. But he has refused to release some of the most dangerous terrorists on the list and has insisted that some of the prisoners not be allowed back into the West Bank for fear that they could travel from there to anywhere in Israel to carry out more terror attacks.Zahar told the demonstrators: “We promise to do all we can for the hero prisoners to return to their homes and families. We have no plans to give up on our prisoners’ freedom. We are close to reaching our goals of releasing the prisoners and having all the refugees return to their homes.” To the prisoners, he said, “We won’t give up on you, and no matter how long it takes, we won’t give up before we see you free.”In response, Amir Gur-Lavie of the Campaign to Free Gilad Schalit said he “doubted the authenticity” of the march to Zahar’s home.Gur-Lavie, who is a neighbor of the Schalit family in the Upper Galilee town of Mitzpe Hila, spoke with The Jerusalem Post after the Herzliya leg of the march.“You can not rally freely in Gaza,” Gur-Lavie said. He added he could only assume that the march was staged by Hamas.Schalit March joined by Israeli astronaut's widowSunday was the seventh day that the Schalit family and their supporters have been on the road. Although they started from Mitzpe Hila on June 27, they stopped walking for Shabbat and resumed their march on Sunday morning toward Herzliya.They were joined there by Rona Ramon, the widow of Israeli astronaut Col. Ilan Ramon, who was killed in the explosion of the Columbia space shuttle in February 2003. Their son, Capt. Assaf Ramon was killed when his F-16 fighter jet crashed in the South Hebron Hills during a training mission last September.As she looked out at the crowd of supporters in Herzliya, Rona Ramon said, “The power of speech is diminished in a place like this. I offer this personal prayer. May it be possible to change what can be changed. Gilad is still alive.”Gilad’s brother Yoel called on the prime minister to conclude a deal for his brother.“I call upon you [Netanyahu] to listen to your nation and to do everything, more than you have done until now, to free my brother,” Yoel Schalit said.The marchers left Kibbutz Shefayim at 9 a.m., causing massive traffic jams as they headed for Herzliya. Highway 4 was closed for the marchers until they reach Kfar Shmaryahu.Drivers cheered the rally despite the traffic jams it caused.After holding two events in Herzliya, the marchers continued onto the Ayalon Highway, where they were joined by thousands of more people.Several lanes on Ayalon South were closed to traffic to allow the marchers to cross safely as they reached the Glilot interchange.On Monday, the family will march past the north Tel Aviv home of Defense Minister Ehud Barak and hold a rally in Kikar Rabin. In the afternoon, they will take a break from marching and travel by car south to the Kerem Shalom area next to Gaza, to visit the spot where Gilad was kidnapped.At 5:30 p.m., conductor Zubin Mehta plans to hold a special performance of the Israel Philharmonic Orchestra in honor of Gilad at the Eshkol National Park near the Gaza border.Mehta said on Sunday he hopes the concert will inspire Gazans to pressure the Hamas government to allow the International Red Cross to visit the soldier for the first time.AP and Jerusalem Post staff contributed to this report.