SYDNEY, Australia — Australia’s new prime minister announced his cabinet on Sunday, replacing the foreign affairs minister and redistributing responsibility for two of the most divisive issues for his party and conservative politics: immigration and climate change.

Scott Morrison, 50, who became prime minister on Friday after a feud inside the governing Liberal Party toppled Malcolm Turnbull, said his “new generation team” would “begin the process of healing.”

“I know this team can deliver the economy we need, the safety we need, and the togetherness we need,” he said.

The appointments include newcomers as well as holdovers. But even as Mr. Morrison promised some continuity, it was clear from his appointments that the rift — which produced Australia’s sixth prime minister since 2010 — is far from resolved and will continue to shape the country.