Shadow Northern Ireland secretary Owen Smith - who unsuccessfully challenged Jeremy Corbyn for leadership of the party in 2016 - was asked to step aside after writing an article calling for a fresh Brexit vote.
Corbyn defended Mear One, the artist who painted the mural, after he posted on Facebook that it was to be scrubbed.
His response suggested the artist was "in good company" because the Rockefeller family had covered over a mural featuring Lenin in their NY development.
Corbyn replied: "Why? You are in good company".
MP Luciana Berger hit out at the "wholly inadequate" explanation and colleague Gavin Shuker said: "It's impossible to confront anti-Semitism in our party if this is the response from the very top".More news: John Dowd, lead lawyer in Russian Federation probe, resigns from Trump's legal team
A spokesman said: "In 2012, Jeremy was responding to concerns about the removal of public art on grounds of freedom of speech". This prompted Corbyn's expression of regret, in which he added that the contents of the mural "are deeply disturbing and anti-Semitic".
Mr Lloyd said: "As we leave the European Union, ensuring there is no hard border between Northern Ireland and the Republic is of paramount importance and this will be my number one priority".
Another said: "This is anti-Semitic imagery which wouldn't be out of place in Der Sturmer".
'I wholeheartedly support its removal. My comment referred to the destruction of the mural "Man at the Crossroads" by Diego Rivera on the Rockefeller Center.
"I'm very, very sorry that people feel hurt by this and that's why I think it's right that Jeremy has expressed regret for it", deputy leader Tom Watson said on the BBC's Andrew Marr Show.
British Jews and an interparliamentary committee of inquiry have dismissed as unsatisfactory an internal Labour audit that largely cleared the party of anti-Semitism allegations.More news: UAE celebrates Pakistan Day
Taking to Twitter, the Pontypridd MP warned the Labour leader that his views on Brexit were shared by others inside the party.
The mural, in east London, depicted a group of businessmen playing a Monopoly-style game on a board balanced on the backs of people.
Labour has been dogged by anti-Semitism rows ever since Mr Corbyn was elected leader in 2015.
Mr Ockerman has denied being anti-Semitic, insisting his mural was about "class and privilege".
It was removed by Tower Hamlets council after a string of complaints were made with ex-mayor Lutfur Rahman saying: "The images of the bankers perpetuate anti-Semitic propaganda about conspiratorial Jewish domination of financial and political institutions".More news: Winter storm watch issued for large swath of Indiana