Mr Bossi, 53, who built the League from a fringe force to the largest party in parliament and a partner in government within a decade, said he would put his leadership to the test at a meeting of the movement's ruling council on 15 September.
'If I am a problem, I shall stand aside,' Corriere della Sera and other newspapers quoted him as saying.
In typically aggressive style, however, he added that if he stayed on as leader: 'I'll stay to clear out (my) enemies.'
Doubts about Mr Bossi's blunt approach rose this week after he stepped off a plane from holiday in Sardinia and claimed that the Prime Minister, Silvio Berlusconi, was pushing for a snap election to rid himself of the League.
His assertion, denied within minutes by the Prime Minister, rested on allegations that media magnate Mr Berlusconi was out to thwart League plans for a federal Italy and tough anti-trust laws that could force him to sell his business empire.
It was widely seen as signalling the end of a brief truce in a slanging match with Mr Berlusconi and more instability for a coalition government which depends on the League for its parliamentary majority.
The claim followed an even more bizarre outburst in which Mr Bossi claimed he had prevented northern anger against corruption in Rome from erupting into armed insurrection in the mid-1980s.
While coalition and opposition politicians ridiculed Mr Bossi's latest tirades, they served to sharpen divisions over his leadership within the League itself.Reuse content