The Foreign Secretary, David Miliband, has accused his shadow, William Hague, of 'playing the man' over the possibility of Tony Blair becoming the president to the EU Council, a new role which will be created after the ratification of the Lisbon Treaty.
Speaking on the programme, Mr Hague said that Conservative opposition to Mr Blair being appointed to the role was based on concerns about the legitimacy of the position.
But Mr Miliband disagreed, saying: "That's just the sort of ad hominem, play the man not the ball, case that does bring politics into disrepute."
Adding that the EU needed to have a "strong voice globally," he said: "We are talking here about the European Council, not a parish council."
Earlier, Mr Hague refused to say if a Conservative government would introduce a referendum on the treaty, adding that the current debate about a role for Mr Blair showed that there should have been a referendum all along.
"People of course are going to say, if the job is that important, that is a major constitutional change and we should have had the referendum that we've all been arguing about for the last few years," he said.
"It leaves people thinking they have not been dealt with honestly and plainly, which of course they have not been dealt with honestly throughout the last four years."
And the two men traded accusations over statements made by Polish MEP Michal Kaminski regarding a massacre of Jews in Poland in 1941.
The row was sparked by comments by Mr Kaminski, who leads the group in the European parliament the Conservative party are members of, that it was "unfair" to compare the massacre at Jedwabne with "Nazi crimes".
"You can't go around hair splitting when it comes to murdering people on the basis of their religion," Mr Miliband said.
But Mr Hague suggested that many of the parties in the Socialist group of which Labour are members have views Mr Miliband would be uncomfortable with, including holocaust denial and homophobia.
"To damage relations with friendly countries in pursuit of a partisan agenda in British politics is not in keeping with the office of British foreign secretary," he said.