Labor will oppose the Turnbull government’s proposed changes to the Senate voting system.

The Labor caucus on Tuesday supported a shadow cabinet decision to oppose the legislation and add an amendment calling for tighter rules on political donations.

The caucus heard 3.3 million people voted for minor parties at the 2013 election and the new laws would lead to their preferences being exhausted.

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Labor’s opposition to the bill, introduced to parliament on Monday, means the government will have to seek the support of the Greens to pass it.

The Greens have signalled their in-principle support, but want to see the result of an inquiry before formally backing it.

However, the minor party wants reform in place before the next election, which is due around September.

The Labor caucus heard the new system would entrench 38 coalition senators as a permanent fixture of the upper house.

Labor frontbencher Penny Wong told the meeting the biggest change to the voting system in three decades should not be the result of a “rushed” deal between the coalition and the Greens.