The group said there were no new developments, but added "a new round will begin" on Sunday.
Negotiators have resumed long-running negotiations in Cairo - brokered by Egypt and Qatar - on pausing Israel's offensive in Gaza in return for freeing hostages.
With an exceptionally large turnout, Saturday's protests are taking place across Israel's major cities; Protesters are also demanding early elections. At a rally in Jerusalem, the father of Israeli-American hostage Hersh Goldberg-Polin said: Politicians must remember, we are fighting for real people
The US - Israel's biggest diplomatic and military ally - is reluctant to back a new offensive that could cause significant civilian casualties, and has insisted on seeing a plan to protect displaced Palestinians first.
The war began after waves of Hamas gunmen stormed across Gaza's border into Israel on 7 October, killing about 1,200 people and taking more than 250 hostages. The group is proscribed as a terrorist organisation by many Western countries.
During the subsequent Israeli military campaign in Gaza, more than 34,600 Palestinians have been killed and over 77,900 wounded, according to figures from the territory's Hamas-run health ministry.
The protests, ahead of the Yom HaShoah Holocaust Remembrance Day, which falls this year on May 6, came as the war in Gaza nears the end of its seventh month amid growing international pressure to stop the fighting.
"The only thing that keeps us going is the hope that Bar is alive and surviving," said Ora Rubinstein, the aunt of Bar Kupershtein, who was seized along with more than 250 others when a Hamas-led attack through Israeli settlements near Gaza on Oct.7.
Tel Aviv, in comparison, has killed more than 34,600 Palestinians and wounded nearly 78,000 amid mass destruction and shortages of necessities in the Palestinian territory.
Netanyahu's government has insisted that it will not stop the war until Hamas is destroyed and all the hostages are returned but intensive efforts are underway to secure a halt to the fighting that might lead to a full ceasefire.
Many of those taken hostage are believed to be dead but families want all of those taken to be brought back.