Arnold Schwarzenegger, the governor of California, has urged Republican presidential candidates to capture the political centre ground ahead of next year’s election by focusing on healthcare reform and education.

As the campaign has unfolded, leading candidates have drifted to the right to win support from social conservatives.

But in an interview with the Financial Times, Mr Schwarzenegger said the party’s candidates were “missing out on something” because televised debates had been dominated by questions about gay marriage, abortion and immigration.

Mr Schwarzenegger said candidates should challenge the questions they were asked in the debates. “Someone has to say: ‘We’ve talked enough about immigration, now I want to talk about healthcare reform’.” The candidates had to “move the agenda”, he said.

Shifting the debates to centre-ground topics would be a positive move, he added. “Being somewhat in the centre . . . is not a detriment. If you sell [your ideas] well and if you explain it well, that’s what leadership is all about, bringing people along.”

The California governor was one of his party’s few successes in last year’s mid-term elections, winning a second term in spite of Republicans losing control of the US Senate and Congress.

His popularity in California, an overwhelmingly liberal state, has surged as he has embraced policies more commonly associated with the Democrats. He has implemented new climate-change legislation and proposed sweeping reform to the state’s health insurance system.

His “post-partisan” stance on these issues was justified by the mandate he won, he said. “I feel because I have good approval ratings, and because I won a Democrat state with 57 per cent of the votes, that . . . I can get people to cross party lines.

“Every decision has to based on what is the best for the people, how can I serve the people, rather than how can I serve my party.”

He said he would welcome a presidential bid from Michael Bloomberg, the mayor of New York, who is considering standing as an independent candidate in next year’s election.

Mr Bloomberg was a “miracle worker” who transcended party lines in running New York, a Democrat party stronghold, Mr Schwarzenegger said.

Mr Bloomberg, elected mayor on a Republican ticket, recently rescinded his party membership, sparking talk he was considering a tilt at the presidency.