Al Jazeera's Sherine Tadros, reporting from the rally in Tel Aviv, said the demonstrators there were trying to send a loud message to the Israeli government that "Gilad Shalit is still alive, and that he should be freed at any price".
Hamas, the Palestinian faction that administers Gaza, has been negotiating with Netanyahu's government since December over the possible release of 1,000 of the more than 7,000 Palestinians held in Israeli prisons in exchange for Shalit's freedom.
Among the major sticking points of the deal, the two sides disagree on which Palestinians should be freed, and where they should be released to.
Only about half of those being offered for release have been chosen by Hamas, and the Palestinian group wants the prisoners returned to their homes in the West Bank.
'Not willing to pay'
Tadros said that Netanyahu "made it very clear in his speech on Thursdaythat there is a price that he's not willing to pay to bring Gilad Shalit home".
"And that [price] is release of prisoners that ... [according to Netanyahu] perhaps could commit more atrocities, could commit more attacks, in Israel," said Tadros.
Osama Hamdan, a senior Hamas spokesman, told Al Jazeera that Netanyahu was coming under pressure from multiple directions over the case.
|Mehta said he hoped the concert would result in the ICRC being given access to Shalit [AFP]
"Netanyahu is under pressure from three sides; internal pressure from his government, which is divided on the issue of releasing Hamas or Palestinian prisoners," he said.
"The second pressure comes from the street, which is created by the family of Gilad Schalit, and also he's facing international pressure. Everyone knows that he will meet with President Obama."
But he said that Hamas' conditions for Shalit's release had not been met. "When Netanyahu says he is ready to set free 1,000 Palestinians, he didn't say that he was ready to release the 450 names which were named by Hamas."
Shalit's captivity has repeatedly come into the public spotlight over the past four years, with one of the stated aims of Israel's war in the Gaza Strip during December 2008-January 2009 being to secure his release.
The recent march across Israel by Shalit's family has reignited debate on the issue and galvanised public support.
Israel's Philharmonic Orchestra held a concert in solidarity with the captured soldier on Monday in the town of Sderot, 3km from the Gaza border.
Zubin Mehta, a renowned US conductor of Indian origin, directed the performance before an expected 10,000-member audience, in a gesture he hoped would result in the International Committee of the Red Cross being given access to Shalit for humanitarian reasons.
"We have an obligation to dream and we want Gilad Shalit, in the first instance, to receive Red Cross visits, and then to be freed as soon as possible," he said.