Sofer, who grew up in this Ocean County town, had recently moved to Israel to begin advanced Torah studies. While hiking Friday with a friend in the Beit Sayit Forest, the two reportedly became separated as they climbed down an embankment, and Sofer could not be found.
His companion spent hours searching before reporting his disappearance to police about 6 p.m., according to the Jerusalem Post.
The forested area was the scene in early July of the revenge killing of a Palestinian teen by Israeli extremists after the abductions and killings of three Israeli teens that Israeli authorities have blamed on the extremist group Hamas, which rules in the Gaza Strip.
Despite a massive manhunt that has included helicopters, search dogs, and thousands of volunteers, Sofer's prolonged disappearance has led to fears he was abducted by Palestinian extremists.
In the Gaza Strip, Hamas and Israeli forces entered a fragile cease-fire Tuesday after seven weeks of off-and-on fighting.
In Jerusalem and in Sofer's hometown, there are fears he would be harmed by possible abductors in retaliation for the conflict.
Sofer's parents, Moshe and Chulba, who traveled to Jerusalem over the weekend to aid in the search, released a video Tuesday offering a reward of 100,000 Israeli shekels, or $28,000, for his safe return.
"I beg of you, please, please, please," his mother cried, her hands shaking as she gripped a reward poster. "If anyone sees [him] please call the police."
At the morning news conference Rep. Christopher Smith (R., Ocean), the mayor of Lakewood, a New York assemblyman, and a New Jersey assemblyman from the area made similar pleas.
Smith, a member of the House Foreign Affairs Committee, said he had already contacted Secretary of State John Kerry's chief of staff to express his "concerns about the possibility of an abduction" as the days pass.
The fact that organizations such as Hamas have not declared they have Sofer in their custody was encouraging, Smith said, but not reassuring, because "such claims are not always made immediately by Hamas."
Smith was followed by New York Assemblyman Dov Hikind, an Orthodox Jew from Brooklyn, who said he was contacted by Sofer's parents soon after they learned of their son's disappearance.
"I have to express my concern that not enough is being done," said Hikind. "I say to the Israeli government, act as if he was an Israeli soldier missing.
"I want the government to use all the resources at its disposal. Imagine what it's like for his mother and father and brothers [to know that] he's disappeared. We are very, very concerned."
Many in the crowd said they did not personally know Aaron Sofer, but came to the news conference in a show of support.
About 55,000 of Lakewood's 93,000 residents are Orthodox Jews. The town became a magnet for strictly Orthodox, or haredi, Jews starting in the 1940s, when Rabbi Aharon Kotler founded a yeshiva, or Torah academy, here called Beth Medrash Govaha.
Among others who addressed the news conference was Rabbi Yisroel Serebrowski, head of Torah Links congregation in Cherry Hill, who said his wife works with Aaron's mother at a Lakewood elementary school.
When he is not occupied studying the Torah, Moshe Sofer runs a small bicycle repair shop, said Serebrowski, describing the parents as extremely close to their 10 children.
"Imagine their distress when they learned their child is missing," Serebrowski said. "They don't know if he's lying in pain, or has been abducted, or is being tortured. . . . Aaron could be any one of us," he said.