He merely stated to the allied commanders that on June 4th his troops would evacuate Genoa or clear their path by the bayonet.
Bonaparte has been reproached for not marching at once to succour Massena: the charge of desertion was brought by Massena and Thiebault, and has been driven home by Lanfrey with his usual skill.

It will, however, scarcely bear a close examination.

The Austrians, at the first trustworthy news of the French inroads into Piedmont and Lombardy, were certain to concentrate either at Turin or Alessandria.
Indeed, Melas was already near Turin, and would have fallen on the First Consul's flank had the latter marched due south towards Genoa.[142] Such a march, with only 40,000 men, would have been perilous: and it could at most only have rescued a now reduced and almost famishing garrison.

Besides, he very naturally expected the besiegers of Genoa to retreat now that their rear was threatened.
Sound policy and a desire to deal a dramatic stroke spurred on the First Consul to a more daring and effective plan; to clear Lombardy of the Imperialists and seize their stores; then, after uniting with Moncey's 15,000 troops, to cut off the retreat of all the Austrian forces west of Milan.
On entering Milan he was greeted with wild acclaim by the partisans of France (June 2nd); they extolled the energy and foresight that brought two armies, as it were down from the clouds, to confound their oppressors.

Numbers of men connected with the Cisalpine Republic had been proscribed, banished, or imprisoned by the Austrians; and their friends now hailed him as the restorer of their republic.