By Tim Castle
LONDON (Reuters) - British Prime Minister David Cameron will try to calm his fractious Conservative party on Tuesday after his worst month in office by stressing his determination to fix an ailing economy in a joint appearance with the leader of his coalition partners.
Cameron will speak alongside Deputy Prime Minister Nick Clegg in a public rebuff to right-wing politicians in his Conservative Party who pin the blame for heavy defeats in local elections last week on his alliance with the Liberal Democrats.
A poorly presented budget, the return of the economy to recession and the loss of more than 400 seats in Thursday's polls have convinced some Conservative lawmakers that Cameron lacks the strategy or competence to lead the party to victory in the next national election in 2015.
Cameron faces further difficulties later this week when two former allies appear at an inquiry into phone hacking.
Seeking to reassert his authority, the Conservative leader will hail the "strong coalition" formed with Clegg's smaller Liberal Democrats two years ago, according to an advance text released by his office.
Speaking at an event in eastern England, Cameron will say he is focused on tackling "a tough task getting even tougher", after data last month showed Britain had fallen back into recession.
"We've got to sort out our debts, get real growth and change this country, so that once again it rewards people who work hard, want to get on and play by the rules. And that's what I am here to do," Cameron will say.
Cameron is under pressure from the right of his party to ignore his centre-left coalition partners and move closer to the UK Independence Party, an anti-European Union fringe party that saw its support rise in last week's elections.
Conservative lawmaker Nadine Dorries warned Cameron at the weekend that he could be deposed by party members who fear his courting of the pro-European Lib Dems will remove any chance of winning power outright in 2015.
Cameron, confident he still has the support of his party's mainstream, ruled out any change in policy on Monday, saying the lesson of the poll defeats was "not about tacking right or moving left".
But any respite Cameron wins from Tuesday's event is likely to be brief. He can expect more negative headlines later this week when two former allies appear at judicial inquiry into a phone hacking scandal at one of Rupert Murdoch's British newspapers.
Rebekah Brooks and Andy Coulson, who both served as News of the World editors, will appear at the Leveson Inquiry on Thursday and Friday.
Coulson moved from the paper to become Cameron's spokesman while Brooks is a former friend of the Conservative leader.
The hacking scandal has prompted searching questions over the close relationship between police, politicians and the press, with Cameron vulnerable to accusations of poor judgment in his dealings with the two former Murdoch executives.
British media have reported that Brooks was willing to release text messages and emails between herself and the prime minister.
(Editing by Jon Hemming)