ROME (AP) _ Socialist Premier Bettino Craxi announced his resignation today, a day after the dominant Christian Democrats withdrew from the governing five-party coalition.

''I am most displeased that given the condition of the government and the majority it was not possible for me to give a political response in the name of the entire government (to solve the crisis),'' Craxi told the Senate.

He then went to Quirinal Palace to present the resignation of his entire Cabinet to President Francesco Cossiga.

It was the second time in five weeks that Craxi tendered his Cabinet's resignation. Craxi resigned March 3 after months of wrangling between his party and the Christian Democrats, but Cossiga rejected the resignation and told Craxi to attempt to keep Italy's 45th postwar government together.

If Cossiga accepts Craxi's resignation this time, he would then have to decide whether to appoint a premier-designate to try to form a government or call parliamentary elections a year ahead of schedule.

Newspapers predicted Cossiga will name a Christian Democrat to govern through early elections.