Opponents also objected to the way the bill was rushed through Parliament, bypassing the normal process that allows for public submissions.
But with Sogavare's supporters in Parliament far outnumbering his opponents, he was able to comfortably get the two-thirds majority he needed for a constitutional change.
Sogavare said the delay would ensure a successful Pacific Games and didn't change anything about how the election would be run.
"The bill is basically to defer the dissolution of Parliament," he said.
Many people in the South Pacific nation of 700,000 remain sceptical of Sogavare's motives, and some worry it could result in more unrest.
Last November, rioting erupted in the capital, Honiara. What began as a peaceful protest against, among other things, the government's decision to switch allegiance from Taiwan to China turned into days of violence, arson and looting. In the aftermath, three bodies were found in a burned-out building.
The following month, Sogavare survived a no-confidence vote in Parliament.
Since then, Sogavare has further cemented his nation's ties with China by signing a new security pact, a move that has alarmed neighbouring countries and others including the US, who fear it could lead to a military buildup in the region.
But Western efforts this year to rebuild relationships with the Solomon Islands have faltered. Sogavare was notably absent from a memorial service in Honiara marking a key World War II battle that was attended by US Deputy Secretary of State Wendy Sherman and other foreign officials.
Then earlier this week, Australian Foreign Minister Penny Wong said her country had offered to pay for the Solomon Islands election to help keep it on track. That drew a swift rebuke from Sogavare, who accused Australia of meddling.
Sogavare said the timing of Wong's statement showed Australia was trying to influence lawmakers to vote against the constitutional amendment.
"This is an assault on our parliamentary democracy and is a direct interference by a foreign government into our domestic affairs," Sogavare said.
Wong told Australian lawmakers it had been a longstanding practice to provide electoral support for the Solomon Islands, and the government had merely been responding to questions from journalists about the latest offer.