"We thank (Kerry) for his efforts. We encourage him and hope to soon achieve positive results," Peres said in remarks broadcast on military radio after two days of verbal attacks against the US secretary of state by Israeli cabinet ministers.
The outburst occurred after Kerry warned on Saturday Israel was facing a growing campaign of delegitimisation which would worsen if peace talks collapsed, referring also to "talk of boycotts."
Cabinet ministers were quick to lash out, describing Kerry's comments as "offensive, unfair and intolerable," and implied Washington was not doing enough to counter "anti-Semitic boycott attempts."
Yesterday, Prime Minister Benjamin Netanyahu sought to calm the situation by acknowledging Kerry's opposition to boycotts and warning his right-wing Likud faction against "personal attacks."
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But late yesterday, US President Barack Obama's National Security Adviser Susan Rice also weighed in on the dispute in several postings on Twitter.
"Personal attacks in Israel directed at Sec Kerry totally unfounded and unacceptable," she wrote.
"US Govt has been clear and consistent that we reject efforts to boycott or legitimise Israel."
Last month, Kerry was subjected to a personal attack by Israel's Defence Minister Moshe Yaalon, who accused him of having a messianic "obsession" with Middle East peace, before being forced to apologise.