"The defense minister had no intention to cause any offense to the secretary, and he apologizes if the secretary was offended by words attributed to the minister," the Defense Ministry said in a statement.
The Jerusalem Post said Washington insisted on an apology.
"Israel and the United States share a common goal to advance the peace talks between Israel and the Palestinians led by Secretary Kerry," the ministry statement said. "We appreciate Secretary Kerry's many efforts toward that end."
The statement did not deny Yaalon made the remarks, attributed to him by Israeli Hebrew-language daily Yedioth Ahronoth, the country's most widely circulated newspaper.
Netanyahu did not address Yaalon's comments directly, but told Parliament Tuesday Washington was "our greatest ally" and said Jerusalem was "working in cooperation" with the White House and State Department.
"We maintain our interests, while cultivating this important tie between the two nations," Netanyahu said. "We strive to reach a true peace accord."
Yedioth Ahronoth triggered the row in an article published Tuesday that quoted Yaalon as saying in private meetings Kerry's diplomatic efforts stemmed from an "incomprehensible obsession" and "a messianic feeling," adding Kerry "can't teach me anything about the conflict with the Palestinians."
Yaalon -- a senior member of Netanyahu's Likud Party who has long taken a hard-line stance on the Palestinian issue -- said Kerry should "take his Nobel Prize and leave us alone," the newspaper said, quoting Yaalon indirectly from unnamed sources.
"The American plan for security arrangements that was shown to us isn't worth the paper it was written on," Yaalon, a former chief of Israel's military, was quoted as saying. "It provides neither security nor peace."
The security arrangements he referred to involve the Jordan Valley, which forms the border between Israel and Jordan in the north and includes the West Bank and eastern parts of Palestinian territories in the south.
Israel insists on a long-term military presence in the valley, which would be the future border with the Palestinian state, something the Palestinian Authority says would compromise Palestinian sovereignty.
The newspaper report quoted Yaalon as saying only a continued Israeli presence in the area would ensure the northern Israeli city of Netanya and Israel's Ben-Gurion Airport did not come under continual rocket attack.
The proposed security arrangements were put together by retired U.S. Gen. John Allen, a former top U.S. commander in Afghanistan who has developed proposals for securing the West Bank if a peace treaty between Israel and the Palestinians is negotiated.
The State Department expressed outrage at Yaalon's reported remarks.
"The remarks of the defense minister, if accurate, are offensive and inappropriate, especially given all that the United States is doing to support Israel's security needs," department spokeswoman Jen Psaki said in a statement.
"Secretary Kerry and his team, including General Allen, have been working day and night to try to promote a secure peace for Israel because of the secretary's deep concern for Israel's future," she said.
"To question his motives and distort his proposals is not something we would expect from the defense minister of a close ally," she said.
Israeli President Shimon Peres expressed support for Kerry's "extraordinary commitment."
"Our deep friendship with the USA is a central component of Israel's security and a force for the advancement of peace in the region," Peres told Israeli lawmakers.