Sajid Javid said the leader of any other mainstream political party would have to go if they did the same.
Questions were raised over the 2014 trip after the Daily Mail published pictures of the Labour leader holding a wreath near the graves of some of those responsible for the massacre of Israeli athletes at the 1972 Munich Olympics.
Labour said that Corbyn had already made clear he was paying his respects to the victims of a 1985 Israeli airstrike on Palestinian Liberation Organisation offices in Tunis.
But the Mail said its own visit to the Martyrs Cemetery had shown the pictures were taken in front of a plaque honouring the founder of Black September, which carried out the Munich atrocity, while the airstrike memorial was 15 yards away.
It quoted from Corbyn’s own account at the time in the Morning Star, in which he said that wreaths had been laid not only at the memorial, but also “on the graves of others killed by Mossad agents in Paris in 1991”.
Responding to the photos, the chair of Jewish Leadership Council, Jonathan Goldstein, told the Jewish News: “This man is not fit to be a Member of Parliament, let alone a national leader.
“He has spent his entire political career cavorting with conspiracy theorists, terrorists and revolutionaries who seek to undo all the good for which our ancestors have given their lives. In so many ways, enough is enough”.
And Javid said in a tweet: “If this was the leader of any other major political party, he or she would be gone by now.”
Labour sources said that Corbyn had already given a full explanation of his presence in the cemetery when the Tunis visit first hit the headlines during last year’s general election campaign.
The Labour leader said at that time: “I was in Tunisia at a Palestinian conference and I spoke at that Palestinian conference and I laid a wreath to all those that had died in the air attack that took place on Tunis, on the headquarters of the Palestinian organisations there.
“And I was accompanied by very many other people who were at a conference searching for peace.”
The pictures emerged amid continuing controversy over Labour’s refusal to adopt in full an international definition of anti-Semitism, including a list of examples of anti-Semitic behaviour.
Three senior union leaders – from the GMB, Unison and Usdaw – have added their voices to calls from deputy leader Tom Watson for the full International Holocaust Remembrance Alliance text to be incorporated in its entirety into Labour’s new code of conduct on anti-Semitism.
Labour has launched a consultation with Jewish groups over the code, after protests that the version agreed by the party’s ruling National Executive Committee omits four examples relating to criticism of the state of Israel.
A Labour Party spokesman said: “The code of conduct adopts the IHRA definition and expands on and contextualises its examples to produce robust, legally sound guidelines that a political party can apply to disciplinary cases.
“The NEC upheld the adoption of the code of conduct on anti-Semitism, but in recognition of the serious concerns expressed, agreed to re-open the development of the code, in consultation with Jewish community organisations and groups, in order to better reflect their views.”
Writing in the Sunday Mirror, shadow chancellor John McDonnell said: “Both Jeremy Corbyn and I have made clear that racism and anti-Semitism have no place in the Labour Party.
“Labour will resolve any outstanding issues within our party and get out there to assist the Jewish community in fighting anti-Semitism and racism.”