CANBERRA—Australia’s conservative government said it would hold national elections on May 18, betting on tax cuts and security spending to fend off a strong challenge by center-left Labor opponents as voters worry that the world’s longest national growth streak shows signs of sputtering.

Kicking off a campaign likely to be dominated by concerns over sliding house prices, drought and the slowing economy, Prime Minister Scott Morrison on Thursday urged voters to rank his economic record above the party-leadership tumult that...