SYDNEY (REUTERS) - Australian Prime Minister Tony Abbott sought a commitment from deputy party leader Julie Bishop that she would not challenge him, Sky News reported on Tuesday, a promise that the Foreign Minister refused to give.

Mr Abbott, 16 months in the top job, has faced a barrage of criticism in recent weeks following a slump in opinion polls, raising speculation that a leadership contest will emerge.

At a meeting on Monday, Mr Abbott sought the promise from Foreign Minister Ms Bishop, Sky News reported.

When asked about the report on Australian television, Mr Abbott declined to refute the account. "What (people) are looking for is politicians who are not endlessly navel gazing, not fighting amongst themselves, but are getting on with the government of this country," Mr Abbott said.

Mr Abbott sought to solidify his leadership on Monday, dropping a signature plan and vowing to engage more collaboratively with colleagues.

In the speech, dubbed by some commentators as the most important of his short tenure, Mr Abbott said he believed he had the full support of Ms Bishop, who along with former Liberal Party leader Malcolm Turnbull, has been touted as a potential replacement.