Albanese will be sworn in as the 31st prime minister on Monday along with four senior party members, even as vote counting continues, before heading to Tokyo to attend a Quad summit on Tuesday with US President Joe Biden and the prime ministers of Japan and India.
The Solomon Islands' recent signing of a security pact with China was a major election issue for outgoing prime minister Scott Morrison, with Western allies concerned it could provide a gateway for a Chinese military presence in the Pacific.
China's foreign minister, Wang Yi, is expected to visit the Solomon Islands this week, local media have reported, although Reuters could not confirm that with Solomon Islands Prime Minister Manasseh Sogavare's office.
In a statement on Sunday, Sogavare said his nation "remains Australia's steadfast friend and development partner of choice".
The Solomon Islands are grateful for Australia's financial, medical and security support over the years, he said, adding "much however, remains to be done".
Sogavare had written to Albanese and "assured him of taking Solomon Islands' relationship with Australia to another level under Albanese's tenure".
Fiji Prime Minister Frank Bainimarama congratulated Albanese in a tweet, writing: "Of your many promises to support the Pacific, none is more welcome than your plan to put the climate first."
New Zealand Prime Minister Jacinda Ardern said that she had called Albanese on Sunday, and that the two countries would continue to work together "deepening our partnership with our close friends in the Pacific, and advancing our interests on the world stage".
"Australia and Aotearoa New Zealand are at our best when we work together," she said.
