While Tony Abbott is convincing voters about his international credentials, the Coalition’s recent momentum is going into reverse, this week’s Essential Report suggests.

The Prime Minister and the government have improved significantly on a number of indicators about its diplomatic competence. Trust in the government’s ability to handle international relations, which fell between November and June, is now back to 40%, a five-point increase in recent months, while lack of trust is down from 59% to 53%, leaving the government essentially where it was in November. However, the response is strongly driven by partisanship, with Labor, Greens and other/Palmer United Party voters all around 70-80% “little or no trust” and Coalition voters with 82% trust. Confidence in Abbott’s ability to represent Australia has also grown a little since June, from 45% to 49%, with a similar partisan split. Perceptions of the government’s handling of relations with Indonesia have also improved, albeit off a low base: 32% of voters think the government’s handling has been good, compared to 39% who rate it as poor, a significant improvement from its 25%-43% rating from voters in May.

But the improvement in voter estimation of the Prime Minister’s diplomatic credentials hasn’t helped the government on voting intention. The Coalition is down a point on its primary vote to 39%, the same level as Labor has been at for several weeks. The Greens are down a point to 9% and PUP is up a point to 4%, for a two-party preferred outcome of 53%-47% to Labor, the same as last week. While the shifts are marginal, it seems clear the momentum that lifted the Coalition’s primary vote to 41% a fortnight ago has dissipated, despite the constant focus on what is supposed to be the Coalition’s strong suit of national security. And that failed to get the government as close to Labor as it managed in the second half of July and August, when a 41% primary vote and a weaker performance from the Greens resulted in a 51%-49% split to Labor. For the moment, national security appears to be providing a sugar hit to the Coalition vote, but not providing a sustained recovery that could see it overhaul the combined Labor-Greens lead.

Essential also asked about perceptions of international relationships. Some 53% of voters believe it’s important to have a close relationship with the United States — the perennial leader on such a question, but down from 57% in June and 60% back in 2011. The UK is rated important by 48%, unchanged; China is on 44%, down two points, then Indonesia on 32%, down three points).

And voters appear to be descending into vagueness on the issue of the republic.

Support for a republic has fallen further to 31% (compared to 41% in 2011) but so has opposition, from 42% in April to 31%, with 38% of voters now declaring they have no opinion.