The row comes against a backdrop of criticism within Labour and in the Jewish community, rejected by party leaders, that Labour has had a persistent problem with anti-Semitism under hard-left leader Jeremy Corbyn.
"Ken Livingstone's comments have been grossly insensitive, and he has caused deep offence and hurt to the Jewish community," Corbyn said in a statement on Wednesday.
Under pressure from Jewish community leaders and Labour members of parliament who argued Livingstone should have been permanently expelled rather than just suspended for two years, Corbyn hinted that further action could be taken.
"Many people are understandably upset that he has continued to make offensive remarks which could open him to further disciplinary action," Corbyn said.
Livingstone got into trouble for saying a year ago that Hitler "was supporting Zionism before he went mad and ended up killing six million Jews".
He was unapologetic after his suspension, saying he had been speaking the truth and likening the disciplinary process to "a court in North Korea".
Labour lawmaker Wes Streeting told Livingstone on BBC news late on Tuesday: "Your poor judgment, your crass remarks and your lack of apology brings the Labour Party into disrepute."
Fellow Labour member of parliament Luciana Berger, who has suffered anti-Semitic abuse, said the party had reached "a new low".
"Why is anti-Semitism being treated differently from any other form of racism?" she wrote on Twitter.
Britain's Chief Rabbi Ephraim Mirvis said the party had failed to show that it was sufficiently serious about tackling anti-Semitism.
"This was a chance for the Labour Party to show that it would not tolerate wilful and unapologetic baiting of the Jewish community," he said in a statement.
The row comes at a time when Labour is profoundly divided over the fundamental goals and direction of the party.
Corbyn, a veteran campaigner once on the fringes of the party, unexpectedly became leader in 2015 on a wave of support from young activists.
He retains strong support from grassroots party members, but many Labour lawmakers see Corbyn as a failed leader who has no chance of winning an election.
Corbyn is a long-standing supporter of the cause of Palestinian rights, which opponents say has given cover to a surge of thinly veiled anti-Semitism among some party activists.
(editing by Stephen Addison)