Kevin Rudd’s agreement with Papua New Guinea on handling asylum seekers has drawn strong support from voters, according to a new poll from Essential Research. And it may have prompted a rise in the Greens’ vote.

Some 61% of voters approve of the PNG deal, compared to 28% who disapprove, with Labor voters most strongly supportive, 75-16%, then Liberal voters on 58-32%. The majority of Greens voters are opposed, 62-32%.

The agreement has significantly altered perceptions of the issue, with 25% of voters now rating Labor’s policy best compared to 26% of voters rating the Liberals’ policy as best — a huge turnaround from June, when the Coalition led 38-13% on the issue. Just 6% of voters think the Greens’ policy is best, but a very large 28% say “none of them”.

More than a third (35%) of voters say the asylum seeker issue is either the most important issue or one of the most important issues in deciding how they’ll vote. This cuts both ways, with 38% of Greens saying it’s the most important or one of the most important, and 39% of Liberal voters.

Malcolm Turnbull has also surged far ahead of Tony Abbott as preferred Liberal leader, with 37% of voters preferring him compared to 17% who prefer Tony Abbott and 10% who prefer Joe Hockey. That’s a rise of seven points for Turnbull since the question was last asked in April 2012, and a fall of six points for Abbott.

On voting intention, Labor’s primary vote remains on 39%, but the Coalition has lost another point to fall to 44%. The Greens has halted their slump, which saw them reach 7%, and have lifted to 9%, suggesting the asylum seeker issue may be playing well for them.

Overall, the two-party preferred outcome remains on 51-49% to the Coalition.